url
stringclasses 147
values | commit
stringclasses 147
values | file_path
stringlengths 7
101
| full_name
stringlengths 1
94
| start
stringlengths 6
10
| end
stringlengths 6
11
| tactic
stringlengths 1
11.2k
| state_before
stringlengths 3
2.09M
| state_after
stringlengths 6
2.09M
|
|---|---|---|---|---|---|---|---|---|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_rem
|
[640, 1]
|
[652, 52]
|
cases br <;> simp
|
sz : ℕ
n m : FinInt sz
br : Bool
r' : FinInt sz
h_full : addfull n m = next br r'
⊢ (match next br r' with
| next false a => toUint n + toUint m
| next true a => toUint n + toUint m - 2 ^ sz) =
if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz
|
case false
sz : ℕ
n m r' : FinInt sz
h_full : addfull n m = next false r'
⊢ toUint n + toUint m = if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz
case true
sz : ℕ
n m r' : FinInt sz
h_full : addfull n m = next true r'
⊢ toUint n + toUint m - 2 ^ sz =
if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_rem
|
[640, 1]
|
[652, 52]
|
. have h := O_lt r'; rw [←h_full] at h
simp [FinInt.addfull_toUint] at h; simp [h]
|
case false
sz : ℕ
n m r' : FinInt sz
h_full : addfull n m = next false r'
⊢ toUint n + toUint m = if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz
case true
sz : ℕ
n m r' : FinInt sz
h_full : addfull n m = next true r'
⊢ toUint n + toUint m - 2 ^ sz =
if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz
|
case true
sz : ℕ
n m r' : FinInt sz
h_full : addfull n m = next true r'
⊢ toUint n + toUint m - 2 ^ sz =
if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_rem
|
[640, 1]
|
[652, 52]
|
. have h := I_not_lt r'; rw [←h_full] at h; sorry
|
case true
sz : ℕ
n m r' : FinInt sz
h_full : addfull n m = next true r'
⊢ toUint n + toUint m - 2 ^ sz =
if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint
|
[654, 1]
|
[658, 16]
|
rw [add_toUint_rem]
|
sz : ℕ
n m : FinInt sz
⊢ toUint (n + m) = mod2 (toUint n + toUint m) sz
|
sz : ℕ
n m : FinInt sz
⊢ (if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz) =
mod2 (toUint n + toUint m) sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint
|
[654, 1]
|
[658, 16]
|
split
|
sz : ℕ
n m : FinInt sz
⊢ (if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz) =
mod2 (toUint n + toUint m) sz
|
case inl
sz : ℕ
n m : FinInt sz
h✝ : toUint n + toUint m < 2 ^ sz
⊢ toUint n + toUint m = mod2 (toUint n + toUint m) sz
case inr
sz : ℕ
n m : FinInt sz
h✝ : ¬toUint n + toUint m < 2 ^ sz
⊢ toUint n + toUint m - 2 ^ sz = mod2 (toUint n + toUint m) sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint
|
[654, 1]
|
[658, 16]
|
. simp [mod2_idem ⟨Int.add_ge_zero _ _ toUint_ge toUint_ge, by assumption⟩]
|
case inl
sz : ℕ
n m : FinInt sz
h✝ : toUint n + toUint m < 2 ^ sz
⊢ toUint n + toUint m = mod2 (toUint n + toUint m) sz
case inr
sz : ℕ
n m : FinInt sz
h✝ : ¬toUint n + toUint m < 2 ^ sz
⊢ toUint n + toUint m - 2 ^ sz = mod2 (toUint n + toUint m) sz
|
case inr
sz : ℕ
n m : FinInt sz
h✝ : ¬toUint n + toUint m < 2 ^ sz
⊢ toUint n + toUint m - 2 ^ sz = mod2 (toUint n + toUint m) sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint
|
[654, 1]
|
[658, 16]
|
. sorry_arith
|
case inr
sz : ℕ
n m : FinInt sz
h✝ : ¬toUint n + toUint m < 2 ^ sz
⊢ toUint n + toUint m - 2 ^ sz = mod2 (toUint n + toUint m) sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint
|
[654, 1]
|
[658, 16]
|
assumption
|
sz : ℕ
n m : FinInt sz
h✝ : toUint n + toUint m < 2 ^ sz
⊢ toUint ?m.152087 + toUint ?m.152089 < 2 ^ ?m.152070
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_cong2
|
[660, 1]
|
[662, 46]
|
simp [cong2, toUint_mod2]
|
sz : ℕ
n m : FinInt sz
⊢ toUint (n + m) ≡ toUint n + toUint m [2^sz]
|
sz : ℕ
n m : FinInt sz
⊢ toUint (n + m) = mod2 (toUint n + toUint m) sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_cong2
|
[660, 1]
|
[662, 46]
|
apply add_toUint
|
sz : ℕ
n m : FinInt sz
⊢ toUint (n + m) = mod2 (toUint n + toUint m) sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
have h := addfull_toSint n m
|
sz : ℕ
n m : FinInt (sz + 1)
⊢ toSint (n + m) =
match n, m with
| next false n', next false m' =>
match n + m with
| next false a => toSint n + toSint m
| next true a => toSint n + toSint m - 2 ^ (sz + 1)
| next false n', next true m' => toSint n + toSint m
| next true n', next false m' => toSint n + toSint m
| next true n', next true m' =>
match n + m with
| next false a => toSint n + toSint m + 2 ^ (sz + 1)
| next true a => toSint n + toSint m
|
sz : ℕ
n m : FinInt (sz + 1)
h :
toSint (addfull n m) =
match n, m with
| next false n', next false m' => toSint n + toSint m
| next false n', next true m' =>
match addfull n m with
| next false a => toSint n + toSint m + 2 ^ (sz + 1)
| next true a => toSint n + toSint m - 2 ^ (sz + 1)
| next true n', next false m' =>
match addfull n m with
| next false a => toSint n + toSint m + 2 ^ (sz + 1)
| next true a => toSint n + toSint m - 2 ^ (sz + 1)
| next true n', next true m' => toSint n + toSint m
⊢ toSint (n + m) =
match n, m with
| next false n', next false m' =>
match n + m with
| next false a => toSint n + toSint m
| next true a => toSint n + toSint m - 2 ^ (sz + 1)
| next false n', next true m' => toSint n + toSint m
| next true n', next false m' => toSint n + toSint m
| next true n', next true m' =>
match n + m with
| next false a => toSint n + toSint m + 2 ^ (sz + 1)
| next true a => toSint n + toSint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
cases n
|
sz : ℕ
n m : FinInt (sz + 1)
h :
toSint (addfull n m) =
match n, m with
| next false n', next false m' => toSint n + toSint m
| next false n', next true m' =>
match addfull n m with
| next false a => toSint n + toSint m + 2 ^ (sz + 1)
| next true a => toSint n + toSint m - 2 ^ (sz + 1)
| next true n', next false m' =>
match addfull n m with
| next false a => toSint n + toSint m + 2 ^ (sz + 1)
| next true a => toSint n + toSint m - 2 ^ (sz + 1)
| next true n', next true m' => toSint n + toSint m
⊢ toSint (n + m) =
match n, m with
| next false n', next false m' =>
match n + m with
| next false a => toSint n + toSint m
| next true a => toSint n + toSint m - 2 ^ (sz + 1)
| next false n', next true m' => toSint n + toSint m
| next true n', next false m' => toSint n + toSint m
| next true n', next true m' =>
match n + m with
| next false a => toSint n + toSint m + 2 ^ (sz + 1)
| next true a => toSint n + toSint m
|
case next
sz : ℕ
m : FinInt (sz + 1)
a✝¹ : Bool
a✝ : FinInt sz
h :
toSint (addfull (next a✝¹ a✝) m) =
match next a✝¹ a✝, m with
| next false n', next false m' => toSint (next a✝¹ a✝) + toSint m
| next false n', next true m' =>
match addfull (next a✝¹ a✝) m with
| next false a => toSint (next a✝¹ a✝) + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next a✝¹ a✝) + toSint m - 2 ^ (sz + 1)
| next true n', next false m' =>
match addfull (next a✝¹ a✝) m with
| next false a => toSint (next a✝¹ a✝) + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next a✝¹ a✝) + toSint m - 2 ^ (sz + 1)
| next true n', next true m' => toSint (next a✝¹ a✝) + toSint m
⊢ toSint (next a✝¹ a✝ + m) =
match next a✝¹ a✝, m with
| next false n', next false m' =>
match next a✝¹ a✝ + m with
| next false a => toSint (next a✝¹ a✝) + toSint m
| next true a => toSint (next a✝¹ a✝) + toSint m - 2 ^ (sz + 1)
| next false n', next true m' => toSint (next a✝¹ a✝) + toSint m
| next true n', next false m' => toSint (next a✝¹ a✝) + toSint m
| next true n', next true m' =>
match next a✝¹ a✝ + m with
| next false a => toSint (next a✝¹ a✝) + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next a✝¹ a✝) + toSint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
case next bn n' =>
cases m; case next bm m' =>
cases bn <;> cases bm <;> simp [addfull] at *
case false.false =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, toSint] at * <;> sorry_arith
case false.true =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
case true.false =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
case true.true =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, toSint] at * <;> sorry_arith
|
sz : ℕ
m : FinInt (sz + 1)
bn : Bool
n' : FinInt sz
h :
toSint (addfull (next bn n') m) =
match next bn n', m with
| next false n'_1, next false m' => toSint (next bn n') + toSint m
| next false n'_1, next true m' =>
match addfull (next bn n') m with
| next false a => toSint (next bn n') + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint m - 2 ^ (sz + 1)
| next true n'_1, next false m' =>
match addfull (next bn n') m with
| next false a => toSint (next bn n') + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint m - 2 ^ (sz + 1)
| next true n'_1, next true m' => toSint (next bn n') + toSint m
⊢ toSint (next bn n' + m) =
match next bn n', m with
| next false n'_1, next false m' =>
match next bn n' + m with
| next false a => toSint (next bn n') + toSint m
| next true a => toSint (next bn n') + toSint m - 2 ^ (sz + 1)
| next false n'_1, next true m' => toSint (next bn n') + toSint m
| next true n'_1, next false m' => toSint (next bn n') + toSint m
| next true n'_1, next true m' =>
match next bn n' + m with
| next false a => toSint (next bn n') + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint m
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
cases m
|
sz : ℕ
m : FinInt (sz + 1)
bn : Bool
n' : FinInt sz
h :
toSint (addfull (next bn n') m) =
match next bn n', m with
| next false n'_1, next false m' => toSint (next bn n') + toSint m
| next false n'_1, next true m' =>
match addfull (next bn n') m with
| next false a => toSint (next bn n') + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint m - 2 ^ (sz + 1)
| next true n'_1, next false m' =>
match addfull (next bn n') m with
| next false a => toSint (next bn n') + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint m - 2 ^ (sz + 1)
| next true n'_1, next true m' => toSint (next bn n') + toSint m
⊢ toSint (next bn n' + m) =
match next bn n', m with
| next false n'_1, next false m' =>
match next bn n' + m with
| next false a => toSint (next bn n') + toSint m
| next true a => toSint (next bn n') + toSint m - 2 ^ (sz + 1)
| next false n'_1, next true m' => toSint (next bn n') + toSint m
| next true n'_1, next false m' => toSint (next bn n') + toSint m
| next true n'_1, next true m' =>
match next bn n' + m with
| next false a => toSint (next bn n') + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint m
|
case next
sz : ℕ
bn : Bool
n' : FinInt sz
a✝¹ : Bool
a✝ : FinInt sz
h :
toSint (addfull (next bn n') (next a✝¹ a✝)) =
match next bn n', next a✝¹ a✝ with
| next false n'_1, next false m' => toSint (next bn n') + toSint (next a✝¹ a✝)
| next false n'_1, next true m' =>
match addfull (next bn n') (next a✝¹ a✝) with
| next false a => toSint (next bn n') + toSint (next a✝¹ a✝) + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint (next a✝¹ a✝) - 2 ^ (sz + 1)
| next true n'_1, next false m' =>
match addfull (next bn n') (next a✝¹ a✝) with
| next false a => toSint (next bn n') + toSint (next a✝¹ a✝) + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint (next a✝¹ a✝) - 2 ^ (sz + 1)
| next true n'_1, next true m' => toSint (next bn n') + toSint (next a✝¹ a✝)
⊢ toSint (next bn n' + next a✝¹ a✝) =
match next bn n', next a✝¹ a✝ with
| next false n'_1, next false m' =>
match next bn n' + next a✝¹ a✝ with
| next false a => toSint (next bn n') + toSint (next a✝¹ a✝)
| next true a => toSint (next bn n') + toSint (next a✝¹ a✝) - 2 ^ (sz + 1)
| next false n'_1, next true m' => toSint (next bn n') + toSint (next a✝¹ a✝)
| next true n'_1, next false m' => toSint (next bn n') + toSint (next a✝¹ a✝)
| next true n'_1, next true m' =>
match next bn n' + next a✝¹ a✝ with
| next false a => toSint (next bn n') + toSint (next a✝¹ a✝) + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint (next a✝¹ a✝)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
case next bm m' =>
cases bn <;> cases bm <;> simp [addfull] at *
case false.false =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, toSint] at * <;> sorry_arith
case false.true =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
case true.false =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
case true.true =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, toSint] at * <;> sorry_arith
|
sz : ℕ
bn : Bool
n' : FinInt sz
bm : Bool
m' : FinInt sz
h :
toSint (addfull (next bn n') (next bm m')) =
match next bn n', next bm m' with
| next false n'_1, next false m'_1 => toSint (next bn n') + toSint (next bm m')
| next false n'_1, next true m'_1 =>
match addfull (next bn n') (next bm m') with
| next false a => toSint (next bn n') + toSint (next bm m') + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint (next bm m') - 2 ^ (sz + 1)
| next true n'_1, next false m'_1 =>
match addfull (next bn n') (next bm m') with
| next false a => toSint (next bn n') + toSint (next bm m') + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint (next bm m') - 2 ^ (sz + 1)
| next true n'_1, next true m'_1 => toSint (next bn n') + toSint (next bm m')
⊢ toSint (next bn n' + next bm m') =
match next bn n', next bm m' with
| next false n'_1, next false m'_1 =>
match next bn n' + next bm m' with
| next false a => toSint (next bn n') + toSint (next bm m')
| next true a => toSint (next bn n') + toSint (next bm m') - 2 ^ (sz + 1)
| next false n'_1, next true m'_1 => toSint (next bn n') + toSint (next bm m')
| next true n'_1, next false m'_1 => toSint (next bn n') + toSint (next bm m')
| next true n'_1, next true m'_1 =>
match next bn n' + next bm m' with
| next false a => toSint (next bn n') + toSint (next bm m') + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint (next bm m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
cases bn <;> cases bm <;> simp [addfull] at *
|
sz : ℕ
bn : Bool
n' : FinInt sz
bm : Bool
m' : FinInt sz
h :
toSint (addfull (next bn n') (next bm m')) =
match next bn n', next bm m' with
| next false n'_1, next false m'_1 => toSint (next bn n') + toSint (next bm m')
| next false n'_1, next true m'_1 =>
match addfull (next bn n') (next bm m') with
| next false a => toSint (next bn n') + toSint (next bm m') + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint (next bm m') - 2 ^ (sz + 1)
| next true n'_1, next false m'_1 =>
match addfull (next bn n') (next bm m') with
| next false a => toSint (next bn n') + toSint (next bm m') + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint (next bm m') - 2 ^ (sz + 1)
| next true n'_1, next true m'_1 => toSint (next bn n') + toSint (next bm m')
⊢ toSint (next bn n' + next bm m') =
match next bn n', next bm m' with
| next false n'_1, next false m'_1 =>
match next bn n' + next bm m' with
| next false a => toSint (next bn n') + toSint (next bm m')
| next true a => toSint (next bn n') + toSint (next bm m') - 2 ^ (sz + 1)
| next false n'_1, next true m'_1 => toSint (next bn n') + toSint (next bm m')
| next true n'_1, next false m'_1 => toSint (next bn n') + toSint (next bm m')
| next true n'_1, next true m'_1 =>
match next bn n' + next bm m' with
| next false a => toSint (next bn n') + toSint (next bm m') + 2 ^ (sz + 1)
| next true a => toSint (next bn n') + toSint (next bm m')
|
case false.false
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next false r)
| next true r => next false (next true r)) =
toSint (next false n') + toSint (next false m')
⊢ toSint (next false n' + next false m') =
match next false n' + next false m' with
| next false a => toSint (next false n') + toSint (next false m')
| next true a => toSint (next false n') + toSint (next false m') - 2 ^ (sz + 1)
case false.true
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r)) =
match
match addfull n' m' with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r) with
| next false a => toSint (next false n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next false n') + toSint (next true m') - 2 ^ (sz + 1)
⊢ toSint (next false n' + next true m') = toSint (next false n') + toSint (next true m')
case true.false
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r)) =
match
match addfull n' m' with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r) with
| next false a => toSint (next true n') + toSint (next false m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next false m') - 2 ^ (sz + 1)
⊢ toSint (next true n' + next false m') = toSint (next true n') + toSint (next false m')
case true.true
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next true (next false r)
| next true r => next true (next true r)) =
toSint (next true n') + toSint (next true m')
⊢ toSint (next true n' + next true m') =
match next true n' + next true m' with
| next false a => toSint (next true n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next true m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
case false.false =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next false r)
| next true r => next false (next true r)) =
toSint (next false n') + toSint (next false m')
⊢ toSint (next false n' + next false m') =
match next false n' + next false m' with
| next false a => toSint (next false n') + toSint (next false m')
| next true a => toSint (next false n') + toSint (next false m') - 2 ^ (sz + 1)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
case false.true =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r)) =
match
match addfull n' m' with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r) with
| next false a => toSint (next false n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next false n') + toSint (next true m') - 2 ^ (sz + 1)
⊢ toSint (next false n' + next true m') = toSint (next false n') + toSint (next true m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
case true.false =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r)) =
match
match addfull n' m' with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r) with
| next false a => toSint (next true n') + toSint (next false m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next false m') - 2 ^ (sz + 1)
⊢ toSint (next true n' + next false m') = toSint (next true n') + toSint (next false m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
case true.true =>
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next true (next false r)
| next true r => next true (next true r)) =
toSint (next true n') + toSint (next true m')
⊢ toSint (next true n' + next true m') =
match next true n' + next true m' with
| next false a => toSint (next true n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next true m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next false r)
| next true r => next false (next true r)) =
toSint (next false n') + toSint (next false m')
⊢ toSint (next false n' + next false m') =
match next false n' + next false m' with
| next false a => toSint (next false n') + toSint (next false m')
| next true a => toSint (next false n') + toSint (next false m') - 2 ^ (sz + 1)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
rw [h'] at h
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next false r)
| next true r => next false (next true r)) =
toSint (next false n') + toSint (next false m')
br : Bool
r : FinInt sz
h' : addfull n' m' = next br r
⊢ toSint (next false n' + next false m') =
match next false n' + next false m' with
| next false a => toSint (next false n') + toSint (next false m')
| next true a => toSint (next false n') + toSint (next false m') - 2 ^ (sz + 1)
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h :
toSint
(match next br r with
| next false r => next false (next false r)
| next true r => next false (next true r)) =
toSint (next false n') + toSint (next false m')
h' : addfull n' m' = next br r
⊢ toSint (next false n' + next false m') =
match next false n' + next false m' with
| next false a => toSint (next false n') + toSint (next false m')
| next true a => toSint (next false n') + toSint (next false m') - 2 ^ (sz + 1)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
cases br <;> simp [bne, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h :
toSint
(match next br r with
| next false r => next false (next false r)
| next true r => next false (next true r)) =
toSint (next false n') + toSint (next false m')
h' : addfull n' m' = next br r
⊢ toSint (next false n' + next false m') =
match next false n' + next false m' with
| next false a => toSint (next false n') + toSint (next false m')
| next true a => toSint (next false n') + toSint (next false m') - 2 ^ (sz + 1)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r)) =
match
match addfull n' m' with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r) with
| next false a => toSint (next false n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next false n') + toSint (next true m') - 2 ^ (sz + 1)
⊢ toSint (next false n' + next true m') = toSint (next false n') + toSint (next true m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
rw [h'] at h
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r)) =
match
match addfull n' m' with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r) with
| next false a => toSint (next false n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next false n') + toSint (next true m') - 2 ^ (sz + 1)
br : Bool
r : FinInt sz
h' : addfull n' m' = next br r
⊢ toSint (next false n' + next true m') = toSint (next false n') + toSint (next true m')
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h :
toSint
(match next br r with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r)) =
match
match next br r with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r) with
| next false a => toSint (next false n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next false n') + toSint (next true m') - 2 ^ (sz + 1)
h' : addfull n' m' = next br r
⊢ toSint (next false n' + next true m') = toSint (next false n') + toSint (next true m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h :
toSint
(match next br r with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r)) =
match
match next br r with
| next false r => next false (next (false != true) r)
| next true r => next true (next (false == true) r) with
| next false a => toSint (next false n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next false n') + toSint (next true m') - 2 ^ (sz + 1)
h' : addfull n' m' = next br r
⊢ toSint (next false n' + next true m') = toSint (next false n') + toSint (next true m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r)) =
match
match addfull n' m' with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r) with
| next false a => toSint (next true n') + toSint (next false m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next false m') - 2 ^ (sz + 1)
⊢ toSint (next true n' + next false m') = toSint (next true n') + toSint (next false m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
rw [h'] at h
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r)) =
match
match addfull n' m' with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r) with
| next false a => toSint (next true n') + toSint (next false m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next false m') - 2 ^ (sz + 1)
br : Bool
r : FinInt sz
h' : addfull n' m' = next br r
⊢ toSint (next true n' + next false m') = toSint (next true n') + toSint (next false m')
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h :
toSint
(match next br r with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r)) =
match
match next br r with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r) with
| next false a => toSint (next true n') + toSint (next false m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next false m') - 2 ^ (sz + 1)
h' : addfull n' m' = next br r
⊢ toSint (next true n' + next false m') = toSint (next true n') + toSint (next false m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
cases br <;> simp [bne, BEq.beq, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h :
toSint
(match next br r with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r)) =
match
match next br r with
| next false r => next false (next (true != false) r)
| next true r => next true (next (true == false) r) with
| next false a => toSint (next true n') + toSint (next false m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next false m') - 2 ^ (sz + 1)
h' : addfull n' m' = next br r
⊢ toSint (next true n' + next false m') = toSint (next true n') + toSint (next false m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
match h': addfull n' m' with
| .next br r =>
rw [h'] at h
cases br <;> simp [bne, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next true (next false r)
| next true r => next true (next true r)) =
toSint (next true n') + toSint (next true m')
⊢ toSint (next true n' + next true m') =
match next true n' + next true m' with
| next false a => toSint (next true n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next true m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
rw [h'] at h
|
sz : ℕ
n' m' : FinInt sz
h :
toSint
(match addfull n' m' with
| next false r => next true (next false r)
| next true r => next true (next true r)) =
toSint (next true n') + toSint (next true m')
br : Bool
r : FinInt sz
h' : addfull n' m' = next br r
⊢ toSint (next true n' + next true m') =
match next true n' + next true m' with
| next false a => toSint (next true n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next true m')
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h :
toSint
(match next br r with
| next false r => next true (next false r)
| next true r => next true (next true r)) =
toSint (next true n') + toSint (next true m')
h' : addfull n' m' = next br r
⊢ toSint (next true n' + next true m') =
match next true n' + next true m' with
| next false a => toSint (next true n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next true m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toSint_msb
|
[664, 1]
|
[703, 59]
|
cases br <;> simp [bne, toSint] at * <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h :
toSint
(match next br r with
| next false r => next true (next false r)
| next true r => next true (next true r)) =
toSint (next true n') + toSint (next true m')
h' : addfull n' m' = next br r
⊢ toSint (next true n' + next true m') =
match next true n' + next true m' with
| next false a => toSint (next true n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next true m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_comm
|
[716, 1]
|
[718, 49]
|
simp [addv]
|
sz : ℕ
n m : FinInt (sz + 1)
⊢ addv n m = addv m n
|
sz : ℕ
n m : FinInt (sz + 1)
⊢ (match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)) =
match m, n with
| next false n', next false m' =>
match m + n with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match m + n with
| next msb r' => (next msb r', !msb)
| x, x_1 => (m + n, false)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_comm
|
[716, 1]
|
[718, 49]
|
cases n
|
sz : ℕ
n m : FinInt (sz + 1)
⊢ (match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)) =
match m, n with
| next false n', next false m' =>
match m + n with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match m + n with
| next msb r' => (next msb r', !msb)
| x, x_1 => (m + n, false)
|
case next
sz : ℕ
m : FinInt (sz + 1)
a✝¹ : Bool
a✝ : FinInt sz
⊢ (match next a✝¹ a✝, m with
| next false n', next false m' =>
match next a✝¹ a✝ + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match next a✝¹ a✝ + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next a✝¹ a✝ + m, false)) =
match m, next a✝¹ a✝ with
| next false n', next false m' =>
match m + next a✝¹ a✝ with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match m + next a✝¹ a✝ with
| next msb r' => (next msb r', !msb)
| x, x_1 => (m + next a✝¹ a✝, false)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_comm
|
[716, 1]
|
[718, 49]
|
cases m
|
case next
sz : ℕ
m : FinInt (sz + 1)
a✝¹ : Bool
a✝ : FinInt sz
⊢ (match next a✝¹ a✝, m with
| next false n', next false m' =>
match next a✝¹ a✝ + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match next a✝¹ a✝ + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next a✝¹ a✝ + m, false)) =
match m, next a✝¹ a✝ with
| next false n', next false m' =>
match m + next a✝¹ a✝ with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match m + next a✝¹ a✝ with
| next msb r' => (next msb r', !msb)
| x, x_1 => (m + next a✝¹ a✝, false)
|
case next.next
sz : ℕ
a✝³ : Bool
a✝² : FinInt sz
a✝¹ : Bool
a✝ : FinInt sz
⊢ (match next a✝³ a✝², next a✝¹ a✝ with
| next false n', next false m' =>
match next a✝³ a✝² + next a✝¹ a✝ with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match next a✝³ a✝² + next a✝¹ a✝ with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next a✝³ a✝² + next a✝¹ a✝, false)) =
match next a✝¹ a✝, next a✝³ a✝² with
| next false n', next false m' =>
match next a✝¹ a✝ + next a✝³ a✝² with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match next a✝¹ a✝ + next a✝³ a✝² with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next a✝¹ a✝ + next a✝³ a✝², false)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_comm
|
[716, 1]
|
[718, 49]
|
case next.next bn n' bm m' =>
simp [add_comm]; cases bn <;> cases bm <;> rfl
|
sz : ℕ
bn : Bool
n' : FinInt sz
bm : Bool
m' : FinInt sz
⊢ (match next bn n', next bm m' with
| next false n'_1, next false m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next bn n' + next bm m', false)) =
match next bm m', next bn n' with
| next false n'_1, next false m'_1 =>
match next bm m' + next bn n' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next bm m' + next bn n' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next bm m' + next bn n', false)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_comm
|
[716, 1]
|
[718, 49]
|
simp [add_comm]
|
sz : ℕ
bn : Bool
n' : FinInt sz
bm : Bool
m' : FinInt sz
⊢ (match next bn n', next bm m' with
| next false n'_1, next false m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next bn n' + next bm m', false)) =
match next bm m', next bn n' with
| next false n'_1, next false m'_1 =>
match next bm m' + next bn n' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next bm m' + next bn n' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next bm m' + next bn n', false)
|
sz : ℕ
bn : Bool
n' : FinInt sz
bm : Bool
m' : FinInt sz
⊢ (match next bn n', next bm m' with
| next false n'_1, next false m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next bn n' + next bm m', false)) =
match next bm m', next bn n' with
| next false n'_1, next false m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next bn n' + next bm m', false)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_comm
|
[716, 1]
|
[718, 49]
|
cases bn <;> cases bm <;> rfl
|
sz : ℕ
bn : Bool
n' : FinInt sz
bm : Bool
m' : FinInt sz
⊢ (match next bn n', next bm m' with
| next false n'_1, next false m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next bn n' + next bm m', false)) =
match next bm m', next bn n' with
| next false n'_1, next false m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next bn n' + next bm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next bn n' + next bm m', false)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
intros h_nov
|
sz : ℕ
n m : FinInt (sz + 1)
⊢ (addv n m).snd = false → toSint (addv n m).fst = toSint n + toSint m
|
sz : ℕ
n m : FinInt (sz + 1)
h_nov : (addv n m).snd = false
⊢ toSint (addv n m).fst = toSint n + toSint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
simp [addv] at *
|
sz : ℕ
n m : FinInt (sz + 1)
h_nov : (addv n m).snd = false
⊢ toSint (addv n m).fst = toSint n + toSint m
|
sz : ℕ
n m : FinInt (sz + 1)
h_nov :
(match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)).snd =
false
⊢ toSint
(match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)).fst =
toSint n + toSint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
have h := add_toSint_msb n m
|
sz : ℕ
n m : FinInt (sz + 1)
h_nov :
(match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)).snd =
false
⊢ toSint
(match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)).fst =
toSint n + toSint m
|
sz : ℕ
n m : FinInt (sz + 1)
h_nov :
(match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)).snd =
false
h :
toSint (n + m) =
match n, m with
| next false n', next false m' =>
match n + m with
| next false a => toSint n + toSint m
| next true a => toSint n + toSint m - 2 ^ (sz + 1)
| next false n', next true m' => toSint n + toSint m
| next true n', next false m' => toSint n + toSint m
| next true n', next true m' =>
match n + m with
| next false a => toSint n + toSint m + 2 ^ (sz + 1)
| next true a => toSint n + toSint m
⊢ toSint
(match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)).fst =
toSint n + toSint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
cases n
|
sz : ℕ
n m : FinInt (sz + 1)
h_nov :
(match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)).snd =
false
h :
toSint (n + m) =
match n, m with
| next false n', next false m' =>
match n + m with
| next false a => toSint n + toSint m
| next true a => toSint n + toSint m - 2 ^ (sz + 1)
| next false n', next true m' => toSint n + toSint m
| next true n', next false m' => toSint n + toSint m
| next true n', next true m' =>
match n + m with
| next false a => toSint n + toSint m + 2 ^ (sz + 1)
| next true a => toSint n + toSint m
⊢ toSint
(match n, m with
| next false n', next false m' =>
match n + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match n + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (n + m, false)).fst =
toSint n + toSint m
|
case next
sz : ℕ
m : FinInt (sz + 1)
a✝¹ : Bool
a✝ : FinInt sz
h_nov :
(match next a✝¹ a✝, m with
| next false n', next false m' =>
match next a✝¹ a✝ + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match next a✝¹ a✝ + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next a✝¹ a✝ + m, false)).snd =
false
h :
toSint (next a✝¹ a✝ + m) =
match next a✝¹ a✝, m with
| next false n', next false m' =>
match next a✝¹ a✝ + m with
| next false a => toSint (next a✝¹ a✝) + toSint m
| next true a => toSint (next a✝¹ a✝) + toSint m - 2 ^ (sz + 1)
| next false n', next true m' => toSint (next a✝¹ a✝) + toSint m
| next true n', next false m' => toSint (next a✝¹ a✝) + toSint m
| next true n', next true m' =>
match next a✝¹ a✝ + m with
| next false a => toSint (next a✝¹ a✝) + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next a✝¹ a✝) + toSint m
⊢ toSint
(match next a✝¹ a✝, m with
| next false n', next false m' =>
match next a✝¹ a✝ + m with
| next msb r' => (next msb r', msb)
| next true n', next true m' =>
match next a✝¹ a✝ + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next a✝¹ a✝ + m, false)).fst =
toSint (next a✝¹ a✝) + toSint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
case next dn n' =>
cases m; case next dm m' =>
cases dn <;> cases dm <;> simp [h] at *
case false.false =>
match h: next false n' + next false m' with
| .next br r =>
rw [h] at h_nov
cases br <;> simp at *
rw [←h]; simp [add_toSint_msb]; simp [h]
case true.true =>
match h: next true n' + next true m' with
| .next br r =>
rw [h] at h_nov
cases br <;> simp at *
rw [←h]; simp [add_toSint_msb]; simp [h]
|
sz : ℕ
m : FinInt (sz + 1)
dn : Bool
n' : FinInt sz
h_nov :
(match next dn n', m with
| next false n'_1, next false m' =>
match next dn n' + m with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m' =>
match next dn n' + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + m, false)).snd =
false
h :
toSint (next dn n' + m) =
match next dn n', m with
| next false n'_1, next false m' =>
match next dn n' + m with
| next false a => toSint (next dn n') + toSint m
| next true a => toSint (next dn n') + toSint m - 2 ^ (sz + 1)
| next false n'_1, next true m' => toSint (next dn n') + toSint m
| next true n'_1, next false m' => toSint (next dn n') + toSint m
| next true n'_1, next true m' =>
match next dn n' + m with
| next false a => toSint (next dn n') + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next dn n') + toSint m
⊢ toSint
(match next dn n', m with
| next false n'_1, next false m' =>
match next dn n' + m with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m' =>
match next dn n' + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + m, false)).fst =
toSint (next dn n') + toSint m
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
cases m
|
sz : ℕ
m : FinInt (sz + 1)
dn : Bool
n' : FinInt sz
h_nov :
(match next dn n', m with
| next false n'_1, next false m' =>
match next dn n' + m with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m' =>
match next dn n' + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + m, false)).snd =
false
h :
toSint (next dn n' + m) =
match next dn n', m with
| next false n'_1, next false m' =>
match next dn n' + m with
| next false a => toSint (next dn n') + toSint m
| next true a => toSint (next dn n') + toSint m - 2 ^ (sz + 1)
| next false n'_1, next true m' => toSint (next dn n') + toSint m
| next true n'_1, next false m' => toSint (next dn n') + toSint m
| next true n'_1, next true m' =>
match next dn n' + m with
| next false a => toSint (next dn n') + toSint m + 2 ^ (sz + 1)
| next true a => toSint (next dn n') + toSint m
⊢ toSint
(match next dn n', m with
| next false n'_1, next false m' =>
match next dn n' + m with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m' =>
match next dn n' + m with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + m, false)).fst =
toSint (next dn n') + toSint m
|
case next
sz : ℕ
dn : Bool
n' : FinInt sz
a✝¹ : Bool
a✝ : FinInt sz
h_nov :
(match next dn n', next a✝¹ a✝ with
| next false n'_1, next false m' =>
match next dn n' + next a✝¹ a✝ with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m' =>
match next dn n' + next a✝¹ a✝ with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + next a✝¹ a✝, false)).snd =
false
h :
toSint (next dn n' + next a✝¹ a✝) =
match next dn n', next a✝¹ a✝ with
| next false n'_1, next false m' =>
match next dn n' + next a✝¹ a✝ with
| next false a => toSint (next dn n') + toSint (next a✝¹ a✝)
| next true a => toSint (next dn n') + toSint (next a✝¹ a✝) - 2 ^ (sz + 1)
| next false n'_1, next true m' => toSint (next dn n') + toSint (next a✝¹ a✝)
| next true n'_1, next false m' => toSint (next dn n') + toSint (next a✝¹ a✝)
| next true n'_1, next true m' =>
match next dn n' + next a✝¹ a✝ with
| next false a => toSint (next dn n') + toSint (next a✝¹ a✝) + 2 ^ (sz + 1)
| next true a => toSint (next dn n') + toSint (next a✝¹ a✝)
⊢ toSint
(match next dn n', next a✝¹ a✝ with
| next false n'_1, next false m' =>
match next dn n' + next a✝¹ a✝ with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m' =>
match next dn n' + next a✝¹ a✝ with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + next a✝¹ a✝, false)).fst =
toSint (next dn n') + toSint (next a✝¹ a✝)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
case next dm m' =>
cases dn <;> cases dm <;> simp [h] at *
case false.false =>
match h: next false n' + next false m' with
| .next br r =>
rw [h] at h_nov
cases br <;> simp at *
rw [←h]; simp [add_toSint_msb]; simp [h]
case true.true =>
match h: next true n' + next true m' with
| .next br r =>
rw [h] at h_nov
cases br <;> simp at *
rw [←h]; simp [add_toSint_msb]; simp [h]
|
sz : ℕ
dn : Bool
n' : FinInt sz
dm : Bool
m' : FinInt sz
h_nov :
(match next dn n', next dm m' with
| next false n'_1, next false m'_1 =>
match next dn n' + next dm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next dn n' + next dm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + next dm m', false)).snd =
false
h :
toSint (next dn n' + next dm m') =
match next dn n', next dm m' with
| next false n'_1, next false m'_1 =>
match next dn n' + next dm m' with
| next false a => toSint (next dn n') + toSint (next dm m')
| next true a => toSint (next dn n') + toSint (next dm m') - 2 ^ (sz + 1)
| next false n'_1, next true m'_1 => toSint (next dn n') + toSint (next dm m')
| next true n'_1, next false m'_1 => toSint (next dn n') + toSint (next dm m')
| next true n'_1, next true m'_1 =>
match next dn n' + next dm m' with
| next false a => toSint (next dn n') + toSint (next dm m') + 2 ^ (sz + 1)
| next true a => toSint (next dn n') + toSint (next dm m')
⊢ toSint
(match next dn n', next dm m' with
| next false n'_1, next false m'_1 =>
match next dn n' + next dm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next dn n' + next dm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + next dm m', false)).fst =
toSint (next dn n') + toSint (next dm m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
cases dn <;> cases dm <;> simp [h] at *
|
sz : ℕ
dn : Bool
n' : FinInt sz
dm : Bool
m' : FinInt sz
h_nov :
(match next dn n', next dm m' with
| next false n'_1, next false m'_1 =>
match next dn n' + next dm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next dn n' + next dm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + next dm m', false)).snd =
false
h :
toSint (next dn n' + next dm m') =
match next dn n', next dm m' with
| next false n'_1, next false m'_1 =>
match next dn n' + next dm m' with
| next false a => toSint (next dn n') + toSint (next dm m')
| next true a => toSint (next dn n') + toSint (next dm m') - 2 ^ (sz + 1)
| next false n'_1, next true m'_1 => toSint (next dn n') + toSint (next dm m')
| next true n'_1, next false m'_1 => toSint (next dn n') + toSint (next dm m')
| next true n'_1, next true m'_1 =>
match next dn n' + next dm m' with
| next false a => toSint (next dn n') + toSint (next dm m') + 2 ^ (sz + 1)
| next true a => toSint (next dn n') + toSint (next dm m')
⊢ toSint
(match next dn n', next dm m' with
| next false n'_1, next false m'_1 =>
match next dn n' + next dm m' with
| next msb r' => (next msb r', msb)
| next true n'_1, next true m'_1 =>
match next dn n' + next dm m' with
| next msb r' => (next msb r', !msb)
| x, x_1 => (next dn n' + next dm m', false)).fst =
toSint (next dn n') + toSint (next dm m')
|
case false.false
sz : ℕ
n' m' : FinInt sz
h_nov :
(match next false n' + next false m' with
| next msb r' => (next msb r', msb)).snd =
false
h : True
⊢ toSint
(match next false n' + next false m' with
| next msb r' => (next msb r', msb)).fst =
toSint (next false n') + toSint (next false m')
case true.true
sz : ℕ
n' m' : FinInt sz
h_nov :
(match next true n' + next true m' with
| next msb r' => (next msb r', !msb)).snd =
false
h : True
⊢ toSint
(match next true n' + next true m' with
| next msb r' => (next msb r', !msb)).fst =
toSint (next true n') + toSint (next true m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
case false.false =>
match h: next false n' + next false m' with
| .next br r =>
rw [h] at h_nov
cases br <;> simp at *
rw [←h]; simp [add_toSint_msb]; simp [h]
|
sz : ℕ
n' m' : FinInt sz
h_nov :
(match next false n' + next false m' with
| next msb r' => (next msb r', msb)).snd =
false
h : True
⊢ toSint
(match next false n' + next false m' with
| next msb r' => (next msb r', msb)).fst =
toSint (next false n') + toSint (next false m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
case true.true =>
match h: next true n' + next true m' with
| .next br r =>
rw [h] at h_nov
cases br <;> simp at *
rw [←h]; simp [add_toSint_msb]; simp [h]
|
sz : ℕ
n' m' : FinInt sz
h_nov :
(match next true n' + next true m' with
| next msb r' => (next msb r', !msb)).snd =
false
h : True
⊢ toSint
(match next true n' + next true m' with
| next msb r' => (next msb r', !msb)).fst =
toSint (next true n') + toSint (next true m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
match h: next false n' + next false m' with
| .next br r =>
rw [h] at h_nov
cases br <;> simp at *
rw [←h]; simp [add_toSint_msb]; simp [h]
|
sz : ℕ
n' m' : FinInt sz
h_nov :
(match next false n' + next false m' with
| next msb r' => (next msb r', msb)).snd =
false
h : True
⊢ toSint
(match next false n' + next false m' with
| next msb r' => (next msb r', msb)).fst =
toSint (next false n') + toSint (next false m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
rw [h] at h_nov
|
sz : ℕ
n' m' : FinInt sz
h_nov :
(match next false n' + next false m' with
| next msb r' => (next msb r', msb)).snd =
false
h✝ : True
br : Bool
r : FinInt sz
h : next false n' + next false m' = next br r
⊢ toSint
(match next br r with
| next msb r' => (next msb r', msb)).fst =
toSint (next false n') + toSint (next false m')
|
sz : ℕ
n' m' : FinInt sz
h✝ : True
br : Bool
r : FinInt sz
h_nov :
(match next br r with
| next msb r' => (next msb r', msb)).snd =
false
h : next false n' + next false m' = next br r
⊢ toSint
(match next br r with
| next msb r' => (next msb r', msb)).fst =
toSint (next false n') + toSint (next false m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
cases br <;> simp at *
|
sz : ℕ
n' m' : FinInt sz
h✝ : True
br : Bool
r : FinInt sz
h_nov :
(match next br r with
| next msb r' => (next msb r', msb)).snd =
false
h : next false n' + next false m' = next br r
⊢ toSint
(match next br r with
| next msb r' => (next msb r', msb)).fst =
toSint (next false n') + toSint (next false m')
|
case false
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next false n' + next false m' = next false r
h_nov : True
⊢ toSint (next false r) = toSint (next false n') + toSint (next false m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
rw [←h]
|
case false
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next false n' + next false m' = next false r
h_nov : True
⊢ toSint (next false r) = toSint (next false n') + toSint (next false m')
|
case false
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next false n' + next false m' = next false r
h_nov : True
⊢ toSint (next false n' + next false m') = toSint (next false n') + toSint (next false m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
simp [add_toSint_msb]
|
case false
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next false n' + next false m' = next false r
h_nov : True
⊢ toSint (next false n' + next false m') = toSint (next false n') + toSint (next false m')
|
case false
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next false n' + next false m' = next false r
h_nov : True
⊢ (match next false n' + next false m' with
| next false a => toSint (next false n') + toSint (next false m')
| next true a => toSint (next false n') + toSint (next false m') - 2 ^ (sz + 1)) =
toSint (next false n') + toSint (next false m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
simp [h]
|
case false
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next false n' + next false m' = next false r
h_nov : True
⊢ (match next false n' + next false m' with
| next false a => toSint (next false n') + toSint (next false m')
| next true a => toSint (next false n') + toSint (next false m') - 2 ^ (sz + 1)) =
toSint (next false n') + toSint (next false m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
match h: next true n' + next true m' with
| .next br r =>
rw [h] at h_nov
cases br <;> simp at *
rw [←h]; simp [add_toSint_msb]; simp [h]
|
sz : ℕ
n' m' : FinInt sz
h_nov :
(match next true n' + next true m' with
| next msb r' => (next msb r', !msb)).snd =
false
h : True
⊢ toSint
(match next true n' + next true m' with
| next msb r' => (next msb r', !msb)).fst =
toSint (next true n') + toSint (next true m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
rw [h] at h_nov
|
sz : ℕ
n' m' : FinInt sz
h_nov :
(match next true n' + next true m' with
| next msb r' => (next msb r', !msb)).snd =
false
h✝ : True
br : Bool
r : FinInt sz
h : next true n' + next true m' = next br r
⊢ toSint
(match next br r with
| next msb r' => (next msb r', !msb)).fst =
toSint (next true n') + toSint (next true m')
|
sz : ℕ
n' m' : FinInt sz
h✝ : True
br : Bool
r : FinInt sz
h_nov :
(match next br r with
| next msb r' => (next msb r', !msb)).snd =
false
h : next true n' + next true m' = next br r
⊢ toSint
(match next br r with
| next msb r' => (next msb r', !msb)).fst =
toSint (next true n') + toSint (next true m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
cases br <;> simp at *
|
sz : ℕ
n' m' : FinInt sz
h✝ : True
br : Bool
r : FinInt sz
h_nov :
(match next br r with
| next msb r' => (next msb r', !msb)).snd =
false
h : next true n' + next true m' = next br r
⊢ toSint
(match next br r with
| next msb r' => (next msb r', !msb)).fst =
toSint (next true n') + toSint (next true m')
|
case true
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next true n' + next true m' = next true r
h_nov : True
⊢ toSint (next true r) = toSint (next true n') + toSint (next true m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
rw [←h]
|
case true
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next true n' + next true m' = next true r
h_nov : True
⊢ toSint (next true r) = toSint (next true n') + toSint (next true m')
|
case true
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next true n' + next true m' = next true r
h_nov : True
⊢ toSint (next true n' + next true m') = toSint (next true n') + toSint (next true m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
simp [add_toSint_msb]
|
case true
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next true n' + next true m' = next true r
h_nov : True
⊢ toSint (next true n' + next true m') = toSint (next true n') + toSint (next true m')
|
case true
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next true n' + next true m' = next true r
h_nov : True
⊢ (match next true n' + next true m' with
| next false a => toSint (next true n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next true m')) =
toSint (next true n') + toSint (next true m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addv_toSint
|
[720, 1]
|
[740, 47]
|
simp [h]
|
case true
sz : ℕ
n' m' : FinInt sz
h✝ : True
r : FinInt sz
h : next true n' + next true m' = next true r
h_nov : True
⊢ (match next true n' + next true m' with
| next false a => toSint (next true n') + toSint (next true m') + 2 ^ (sz + 1)
| next true a => toSint (next true n') + toSint (next true m')) =
toSint (next true n') + toSint (next true m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_toUint
|
[752, 1]
|
[754, 8]
|
sorry
|
sz : ℕ
n : FinInt sz
⊢ toUint (-n) = mod2 (-toUint n) sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_toUint_cong2
|
[756, 1]
|
[758, 46]
|
simp [cong2, toUint_mod2]
|
sz : ℕ
n : FinInt sz
⊢ toUint (-n) ≡ -toUint n [2^sz]
|
sz : ℕ
n : FinInt sz
⊢ toUint (-n) = mod2 (-toUint n) sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_toUint_cong2
|
[756, 1]
|
[758, 46]
|
apply neg_toUint
|
sz : ℕ
n : FinInt sz
⊢ toUint (-n) = mod2 (-toUint n) sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_minusOne
|
[760, 1]
|
[771, 18]
|
match H: sz with
| 0 => decide
| sz'+1 =>
have h: sz' + 1 > 0 := by sorry_arith
apply eq_of_toUint_cong2
simp [toUint_minusOne]
simp [neg_toUint]
apply cong2_mod2_left
simp [ofInt_1, toUint_one h]
sorry_arith
|
sz : ℕ
⊢ -1 = minusOne
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_minusOne
|
[760, 1]
|
[771, 18]
|
decide
|
sz : ℕ
H : sz = 0
⊢ -1 = minusOne
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_minusOne
|
[760, 1]
|
[771, 18]
|
have h: sz' + 1 > 0 := by sorry_arith
|
sz sz' : ℕ
H : sz = Nat.succ sz'
⊢ -1 = minusOne
|
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ -1 = minusOne
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_minusOne
|
[760, 1]
|
[771, 18]
|
apply eq_of_toUint_cong2
|
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ -1 = minusOne
|
case a
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ toUint (-1) ≡ toUint minusOne [2^sz' + 1]
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_minusOne
|
[760, 1]
|
[771, 18]
|
simp [toUint_minusOne]
|
case a
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ toUint (-1) ≡ toUint minusOne [2^sz' + 1]
|
case a
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ toUint (-1) ≡ 2 ^ sz' + (2 ^ sz' - 1) [2^sz' + 1]
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_minusOne
|
[760, 1]
|
[771, 18]
|
simp [neg_toUint]
|
case a
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ toUint (-1) ≡ 2 ^ sz' + (2 ^ sz' - 1) [2^sz' + 1]
|
case a
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ mod2 (-toUint 1) (sz' + 1) ≡ 2 ^ sz' + (2 ^ sz' - 1) [2^sz' + 1]
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_minusOne
|
[760, 1]
|
[771, 18]
|
apply cong2_mod2_left
|
case a
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ mod2 (-toUint 1) (sz' + 1) ≡ 2 ^ sz' + (2 ^ sz' - 1) [2^sz' + 1]
|
case a.a
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ (-toUint 1) ≡ 2 ^ sz' + (2 ^ sz' - 1) [2^sz' + 1]
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_minusOne
|
[760, 1]
|
[771, 18]
|
sorry_arith
|
case a.a
sz sz' : ℕ
H : sz = Nat.succ sz'
h : sz' + 1 > 0
⊢ (-toUint 1) ≡ 2 ^ sz' + (2 ^ sz' - 1) [2^sz' + 1]
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.neg_minusOne
|
[760, 1]
|
[771, 18]
|
sorry_arith
|
sz sz' : ℕ
H : sz = Nat.succ sz'
⊢ sz' + 1 > 0
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_eq_xor_minusOne
|
[773, 1]
|
[782, 40]
|
simp [neg_minusOne, HXor.hXor]
|
sz : ℕ
n : FinInt sz
⊢ comp n = n ^^^ -1
|
sz : ℕ
n : FinInt sz
⊢ comp n = xor n minusOne
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_eq_xor_minusOne
|
[773, 1]
|
[782, 40]
|
induction sz <;> simp [comp, xor, logic1, logic2, minusOne] at *
|
sz : ℕ
n : FinInt sz
⊢ comp n = xor n minusOne
|
case zero
n : FinInt Nat.zero
⊢ logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n nil
case succ
n✝ : ℕ
n_ih✝ : ∀ (n : FinInt n✝), logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n minusOne
n : FinInt (Nat.succ n✝)
⊢ logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n (I minusOne)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_eq_xor_minusOne
|
[773, 1]
|
[782, 40]
|
case zero =>
cases n; simp
|
n : FinInt Nat.zero
⊢ logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n nil
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_eq_xor_minusOne
|
[773, 1]
|
[782, 40]
|
case succ sz ih =>
match n with
| .I m => simp [logic1, logic2, ih]
| .O m => simp [logic1, logic2, ih]
|
sz : ℕ
ih : ∀ (n : FinInt sz), logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n minusOne
n : FinInt (Nat.succ sz)
⊢ logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n (I minusOne)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_eq_xor_minusOne
|
[773, 1]
|
[782, 40]
|
cases n
|
n : FinInt Nat.zero
⊢ logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n nil
|
case nil
⊢ logic1 (fun x => !x) nil = logic2 (fun x x_1 => x != x_1) nil nil
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_eq_xor_minusOne
|
[773, 1]
|
[782, 40]
|
simp
|
case nil
⊢ logic1 (fun x => !x) nil = logic2 (fun x x_1 => x != x_1) nil nil
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_eq_xor_minusOne
|
[773, 1]
|
[782, 40]
|
match n with
| .I m => simp [logic1, logic2, ih]
| .O m => simp [logic1, logic2, ih]
|
sz : ℕ
ih : ∀ (n : FinInt sz), logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n minusOne
n : FinInt (Nat.succ sz)
⊢ logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n (I minusOne)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_eq_xor_minusOne
|
[773, 1]
|
[782, 40]
|
simp [logic1, logic2, ih]
|
sz : ℕ
ih : ∀ (n : FinInt sz), logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n minusOne
n : FinInt (Nat.succ sz)
m : FinInt sz
⊢ logic1 (fun x => !x) (I m) = logic2 (fun x x_1 => x != x_1) (I m) (I minusOne)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_eq_xor_minusOne
|
[773, 1]
|
[782, 40]
|
simp [logic1, logic2, ih]
|
sz : ℕ
ih : ∀ (n : FinInt sz), logic1 (fun x => !x) n = logic2 (fun x x_1 => x != x_1) n minusOne
n : FinInt (Nat.succ sz)
m : FinInt sz
⊢ logic1 (fun x => !x) (O m) = logic2 (fun x x_1 => x != x_1) (O m) (I minusOne)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.sub_toUint
|
[794, 1]
|
[796, 8]
|
sorry
|
sz : ℕ
n m : FinInt sz
⊢ toUint (n - m) = mod2 (toUint n - toUint m) sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.sub_toUint_cong2
|
[798, 1]
|
[800, 46]
|
simp [cong2, toUint_mod2]
|
sz : ℕ
m n : FinInt sz
⊢ toUint (n - m) ≡ toUint n - toUint m [2^sz]
|
sz : ℕ
m n : FinInt sz
⊢ toUint (n - m) = mod2 (toUint n - toUint m) sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.sub_toUint_cong2
|
[798, 1]
|
[800, 46]
|
apply sub_toUint
|
sz : ℕ
m n : FinInt sz
⊢ toUint (n - m) = mod2 (toUint n - toUint m) sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.zext_toUint
|
[811, 1]
|
[812, 28]
|
simp [zext, toUint_ofInt]
|
sz₁ sz₂ : ℕ
n : FinInt sz₁
⊢ toUint (zext sz₂ n) = mod2 (toUint n) sz₂
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.zext_toUint'
|
[814, 1]
|
[815, 8]
|
sorry
|
sz₁ sz₂ : ℕ
n : FinInt sz₁
⊢ sz₁ < sz₂ → toUint (zext sz₂ n) = toUint n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[LHS]
|
r₁ r₂ : Region scf
b : Bool
⊢ run ⟦ LHS r₁ r₂ ⟧ (INPUT b) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(denoteRegion scf
(Region.mk "entry" []
[Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])])
[])
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[run_denoteRegion]
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(denoteRegion scf
(Region.mk "entry" []
[Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])])
[])
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(do
denoteTypedArgs [] []
denoteOps scf
[Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])])
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
rw[run_seq]
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(do
denoteTypedArgs [] []
denoteOps scf
[Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])])
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ (match run (denoteTypedArgs [] []) (INPUT b) with
| Except.ok (PUnit.unit, env') =>
run
(denoteOps scf
[Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])])
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[run_denoteTypedArgs_nil]
|
r₁ r₂ : Region scf
b : Bool
⊢ (match run (denoteTypedArgs [] []) (INPUT b) with
| Except.ok (PUnit.unit, env') =>
run
(denoteOps scf
[Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])])
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(denoteOps scf
[Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])])
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp [run_denoteOps_singleton]
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(denoteOps scf
[Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])])
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(denoteOp scf
(Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])))
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[run_denoteOp]
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(denoteOp scf
(Op.mk "scf.if" [] [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)] [r₁, r₂] (AttrDict.mk [])))
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(do
let args ← denoteOpArgs scf [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)]
OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] args (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[run_bind]
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(do
let args ← denoteOpArgs scf [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)]
OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] args (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
(INPUT b) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)]) (INPUT b) with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[run_denoteOpArgs_cons_]
|
r₁ r₂ : Region scf
b : Bool
⊢ (match run (denoteOpArgs scf [(SSAVal.SSAVal "b", MLIRType.int Signedness.Signless 1)]) (INPUT b) with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
run
(do
let x ← TopM.get (MLIRType.int Signedness.Signless 1) (SSAVal.SSAVal "b")
let xs ← denoteOpArgs scf []
pure ({ fst := MLIRType.int Signedness.Signless 1, snd := x } :: xs))
(INPUT b) with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[run_bind]
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
run
(do
let x ← TopM.get (MLIRType.int Signedness.Signless 1) (SSAVal.SSAVal "b")
let xs ← denoteOpArgs scf []
pure ({ fst := MLIRType.int Signedness.Signless 1, snd := x } :: xs))
(INPUT b) with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
match run (TopM.get (MLIRType.int Signedness.Signless 1) (SSAVal.SSAVal "b")) (INPUT b) with
| Except.ok (a, env') =>
match run (denoteOpArgs scf []) env' with
| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.int Signedness.Signless 1, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[INPUT]
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
match run (TopM.get (MLIRType.int Signedness.Signless 1) (SSAVal.SSAVal "b")) (INPUT b) with
| Except.ok (a, env') =>
match run (denoteOpArgs scf []) env' with
| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.int Signedness.Signless 1, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) [])) (INPUT b)
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
match
run (TopM.get (MLIRType.int Signedness.Signless 1) (SSAVal.SSAVal "b"))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| Except.ok (a, env') =>
match run (denoteOpArgs scf []) env' with
| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.int Signedness.Signless 1, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) []))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
rw[run_TopM_get_]
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
match
run (TopM.get (MLIRType.int Signedness.Signless 1) (SSAVal.SSAVal "b"))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| Except.ok (a, env') =>
match run (denoteOpArgs scf []) env' with
| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.int Signedness.Signless 1, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) []))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
match
Except.ok
(match
SSAEnv.get (SSAVal.SSAVal "b") (MLIRType.int Signedness.Signless 1)
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| some v => v
| none => default,
SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| Except.ok (a, env') =>
match run (denoteOpArgs scf []) env' with
| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.int Signedness.Signless 1, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) []))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[SSAEnv.get_set_eq]
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
match
Except.ok
(match
SSAEnv.get (SSAVal.SSAVal "b") (MLIRType.int Signedness.Signless 1)
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| some v => v
| none => default,
SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| Except.ok (a, env') =>
match run (denoteOpArgs scf []) env' with
| Except.ok (a_1, env') => run (pure ({ fst := MLIRType.int Signedness.Signless 1, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) []))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
match
run (denoteOpArgs scf [])
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| Except.ok (a, env') =>
run (pure ({ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 } :: a)) env'
| Except.error e => Except.error e with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) []))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[run_denoteOpArgs_nil]
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
match
run (denoteOpArgs scf [])
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| Except.ok (a, env') =>
run (pure ({ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 } :: a)) env'
| Except.error e => Except.error e with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) []))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
run (pure [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }])
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) []))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Dialects/ScfSemantics.lean
|
SCF.IF.equivalent
|
[100, 1]
|
[149, 10]
|
simp[run_pure]
|
r₁ r₂ : Region scf
b : Bool
⊢ (match
run (pure [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }])
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) with
| Except.ok (a, env') =>
run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op (IOp.mk "scf.if" [] a (OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
env'
| Except.error e => Except.error e) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) []))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
|
r₁ r₂ : Region scf
b : Bool
⊢ run
(OpM.toTopM (TopM.mapDenoteRegion scf [r₁, r₂])
(Semantics.semantics_op
(IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }]
(OpM.denoteRegions [r₁, r₂] 0) (AttrDict.mk []))))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) =
run (TopM.scoped (denoteRegion scf (if b = true then r₁ else r₂) []))
(SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
|
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