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.eq_of_toUint_eq
|
[434, 1]
|
[446, 28]
|
cases a
|
sz : ℕ
ih : ∀ (a b : FinInt sz), toUint a = toUint b → a = b
a b : FinInt (Nat.succ sz)
h : toUint a = toUint b
⊢ a = b
|
case next
n✝ : ℕ
a✝¹ : Bool
a✝ : FinInt n✝
ih : ∀ (a b : FinInt (Nat.add n✝ 0)), toUint a = toUint b → a = b
b : FinInt (Nat.succ (Nat.add n✝ 0))
h : toUint (next a✝¹ a✝) = toUint b
⊢ next a✝¹ a✝ = b
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_eq
|
[434, 1]
|
[446, 28]
|
case next sz da a' =>
cases b; case next db b' =>
cases da <;> cases db <;> simp [toUint] at h <;> simp
. apply ih _ _ h
. have h₁ := @toUint_lt _ a'; have h₂ := @toUint_ge _ b'; sorry_arith
. have h₁ := @toUint_ge _ a'; have h₂ := @toUint_lt _ b'; sorry_arith
. apply ih; sorry_arith
|
sz : ℕ
da : Bool
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b : FinInt (Nat.succ (Nat.add sz 0))
h : toUint (next da a') = toUint b
⊢ next da a' = b
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_eq
|
[434, 1]
|
[446, 28]
|
cases b
|
sz : ℕ
da : Bool
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b : FinInt (Nat.succ (Nat.add sz 0))
h : toUint (next da a') = toUint b
⊢ next da a' = b
|
case next
sz : ℕ
da : Bool
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
a✝¹ : Bool
a✝ : FinInt sz
h : toUint (next da a') = toUint (next a✝¹ a✝)
⊢ next da a' = next a✝¹ a✝
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_eq
|
[434, 1]
|
[446, 28]
|
case next db b' =>
cases da <;> cases db <;> simp [toUint] at h <;> simp
. apply ih _ _ h
. have h₁ := @toUint_lt _ a'; have h₂ := @toUint_ge _ b'; sorry_arith
. have h₁ := @toUint_ge _ a'; have h₂ := @toUint_lt _ b'; sorry_arith
. apply ih; sorry_arith
|
sz : ℕ
da : Bool
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
db : Bool
b' : FinInt sz
h : toUint (next da a') = toUint (next db b')
⊢ next da a' = next db b'
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_eq
|
[434, 1]
|
[446, 28]
|
cases da <;> cases db <;> simp [toUint] at h <;> simp
|
sz : ℕ
da : Bool
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
db : Bool
b' : FinInt sz
h : toUint (next da a') = toUint (next db b')
⊢ next da a' = next db b'
|
case false.false
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
case false.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = 2 ^ sz + toUint b'
⊢ False
case true.false
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : 2 ^ sz + toUint a' = toUint b'
⊢ False
case true.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_eq
|
[434, 1]
|
[446, 28]
|
. apply ih _ _ h
|
case false.false
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
case false.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = 2 ^ sz + toUint b'
⊢ False
case true.false
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : 2 ^ sz + toUint a' = toUint b'
⊢ False
case true.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
|
case false.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = 2 ^ sz + toUint b'
⊢ False
case true.false
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : 2 ^ sz + toUint a' = toUint b'
⊢ False
case true.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_eq
|
[434, 1]
|
[446, 28]
|
. have h₁ := @toUint_lt _ a'; have h₂ := @toUint_ge _ b'; sorry_arith
|
case false.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = 2 ^ sz + toUint b'
⊢ False
case true.false
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : 2 ^ sz + toUint a' = toUint b'
⊢ False
case true.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
|
case true.false
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : 2 ^ sz + toUint a' = toUint b'
⊢ False
case true.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_eq
|
[434, 1]
|
[446, 28]
|
. have h₁ := @toUint_ge _ a'; have h₂ := @toUint_lt _ b'; sorry_arith
|
case true.false
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : 2 ^ sz + toUint a' = toUint b'
⊢ False
case true.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
|
case true.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_eq
|
[434, 1]
|
[446, 28]
|
. apply ih; sorry_arith
|
case true.true
sz : ℕ
a' : FinInt sz
ih : ∀ (a b : FinInt (Nat.add sz 0)), toUint a = toUint b → a = b
b' : FinInt sz
h : toUint a' = toUint b'
⊢ a' = b'
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_cong2
|
[448, 1]
|
[452, 52]
|
intros h
|
n : ℕ
a b : FinInt n
⊢ toUint a ≡ toUint b [2^n] → a = b
|
n : ℕ
a b : FinInt n
h : toUint a ≡ toUint b [2^n]
⊢ a = b
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_cong2
|
[448, 1]
|
[452, 52]
|
apply eq_of_toUint_eq
|
n : ℕ
a b : FinInt n
h : toUint a ≡ toUint b [2^n]
⊢ a = b
|
case a
n : ℕ
a b : FinInt n
h : toUint a ≡ toUint b [2^n]
⊢ toUint a = toUint b
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.eq_of_toUint_cong2
|
[448, 1]
|
[452, 52]
|
apply cong2_to_eq n h toUint_bounds toUint_bounds
|
case a
n : ℕ
a b : FinInt n
h : toUint a ≡ toUint b [2^n]
⊢ toUint a = toUint b
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
induction sz
|
sz : ℕ
n : FinInt sz
⊢ toUint (comp n) = 2 ^ sz - 1 - toUint n
|
case zero
n : FinInt Nat.zero
⊢ toUint (comp n) = 2 ^ Nat.zero - 1 - toUint n
case succ
n✝ : ℕ
n_ih✝ : ∀ (n : FinInt n✝), toUint (comp n) = 2 ^ n✝ - 1 - toUint n
n : FinInt (Nat.succ n✝)
⊢ toUint (comp n) = 2 ^ Nat.succ n✝ - 1 - toUint n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
case zero =>
cases n; simp
|
n : FinInt Nat.zero
⊢ toUint (comp n) = 2 ^ Nat.zero - 1 - toUint n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
case succ sz ih =>
simp [comp] at ih
cases n; case next sz bn n' =>
cases bn <;> simp [ih]
. sorry_arith
. sorry_arith
|
sz : ℕ
ih : ∀ (n : FinInt sz), toUint (comp n) = 2 ^ sz - 1 - toUint n
n : FinInt (Nat.succ sz)
⊢ toUint (comp n) = 2 ^ Nat.succ sz - 1 - toUint n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
cases n
|
n : FinInt Nat.zero
⊢ toUint (comp n) = 2 ^ Nat.zero - 1 - toUint n
|
case nil
⊢ toUint (comp nil) = 2 ^ Nat.zero - 1 - toUint nil
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
simp
|
case nil
⊢ toUint (comp nil) = 2 ^ Nat.zero - 1 - toUint nil
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
simp [comp] at ih
|
sz : ℕ
ih : ∀ (n : FinInt sz), toUint (comp n) = 2 ^ sz - 1 - toUint n
n : FinInt (Nat.succ sz)
⊢ toUint (comp n) = 2 ^ Nat.succ sz - 1 - toUint n
|
sz : ℕ
ih : ∀ (n : FinInt sz), toUint (logic1 (fun x => !x) n) = 2 ^ sz - 1 - toUint n
n : FinInt (Nat.succ sz)
⊢ toUint (comp n) = 2 ^ Nat.succ sz - 1 - toUint n
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
cases n
|
sz : ℕ
ih : ∀ (n : FinInt sz), toUint (logic1 (fun x => !x) n) = 2 ^ sz - 1 - toUint n
n : FinInt (Nat.succ sz)
⊢ toUint (comp n) = 2 ^ Nat.succ sz - 1 - toUint n
|
case next
n✝ : ℕ
a✝¹ : Bool
a✝ : FinInt n✝
ih : ∀ (n : FinInt (Nat.add n✝ 0)), toUint (logic1 (fun x => !x) n) = 2 ^ Nat.add n✝ 0 - 1 - toUint n
⊢ toUint (comp (next a✝¹ a✝)) = 2 ^ Nat.succ (Nat.add n✝ 0) - 1 - toUint (next a✝¹ a✝)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
case next sz bn n' =>
cases bn <;> simp [ih]
. sorry_arith
. sorry_arith
|
sz : ℕ
bn : Bool
n' : FinInt sz
ih : ∀ (n : FinInt (Nat.add sz 0)), toUint (logic1 (fun x => !x) n) = 2 ^ Nat.add sz 0 - 1 - toUint n
⊢ toUint (comp (next bn n')) = 2 ^ Nat.succ (Nat.add sz 0) - 1 - toUint (next bn n')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
cases bn <;> simp [ih]
|
sz : ℕ
bn : Bool
n' : FinInt sz
ih : ∀ (n : FinInt (Nat.add sz 0)), toUint (logic1 (fun x => !x) n) = 2 ^ Nat.add sz 0 - 1 - toUint n
⊢ toUint (comp (next bn n')) = 2 ^ Nat.succ (Nat.add sz 0) - 1 - toUint (next bn n')
|
case false
sz : ℕ
n' : FinInt sz
ih : ∀ (n : FinInt (Nat.add sz 0)), toUint (logic1 (fun x => !x) n) = 2 ^ Nat.add sz 0 - 1 - toUint n
⊢ 2 ^ sz + (2 ^ sz - 1 - toUint n') = 2 ^ Nat.succ sz - 1 - toUint n'
case true
sz : ℕ
n' : FinInt sz
ih : ∀ (n : FinInt (Nat.add sz 0)), toUint (logic1 (fun x => !x) n) = 2 ^ Nat.add sz 0 - 1 - toUint n
⊢ 2 ^ sz - 1 - toUint n' = 2 ^ Nat.succ sz - 1 - (2 ^ sz + toUint n')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
. sorry_arith
|
case false
sz : ℕ
n' : FinInt sz
ih : ∀ (n : FinInt (Nat.add sz 0)), toUint (logic1 (fun x => !x) n) = 2 ^ Nat.add sz 0 - 1 - toUint n
⊢ 2 ^ sz + (2 ^ sz - 1 - toUint n') = 2 ^ Nat.succ sz - 1 - toUint n'
case true
sz : ℕ
n' : FinInt sz
ih : ∀ (n : FinInt (Nat.add sz 0)), toUint (logic1 (fun x => !x) n) = 2 ^ Nat.add sz 0 - 1 - toUint n
⊢ 2 ^ sz - 1 - toUint n' = 2 ^ Nat.succ sz - 1 - (2 ^ sz + toUint n')
|
case true
sz : ℕ
n' : FinInt sz
ih : ∀ (n : FinInt (Nat.add sz 0)), toUint (logic1 (fun x => !x) n) = 2 ^ Nat.add sz 0 - 1 - toUint n
⊢ 2 ^ sz - 1 - toUint n' = 2 ^ Nat.succ sz - 1 - (2 ^ sz + toUint n')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.comp_toUint
|
[487, 1]
|
[497, 18]
|
. sorry_arith
|
case true
sz : ℕ
n' : FinInt sz
ih : ∀ (n : FinInt (Nat.add sz 0)), toUint (logic1 (fun x => !x) n) = 2 ^ Nat.add sz 0 - 1 - toUint n
⊢ 2 ^ sz - 1 - toUint n' = 2 ^ Nat.succ sz - 1 - (2 ^ sz + toUint n')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
revert n m
|
sz : ℕ
n m : FinInt sz
⊢ toUint (addfull n m) = toUint n + toUint m
|
sz : ℕ
⊢ ∀ (n m : FinInt sz), toUint (addfull n m) = toUint n + toUint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
induction sz <;> intros n m
|
sz : ℕ
⊢ ∀ (n m : FinInt sz), toUint (addfull n m) = toUint n + toUint m
|
case zero
n m : FinInt Nat.zero
⊢ toUint (addfull n m) = toUint n + toUint m
case succ
n✝ : ℕ
n_ih✝ : ∀ (n m : FinInt n✝), toUint (addfull n m) = toUint n + toUint m
n m : FinInt (Nat.succ n✝)
⊢ toUint (addfull n m) = toUint n + toUint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
case zero =>
cases n; cases m; simp [addfull]
|
n m : FinInt Nat.zero
⊢ toUint (addfull n m) = toUint n + toUint m
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
case succ sz ih =>
cases n; case next sz dn n' =>
cases m; case next dm m' =>
simp [addfull]
split
case h_1 r h =>
have h': r.toUint = n'.toUint + m'.toUint := by
rw [←ih n' m']; simp [h]
simp at h'
cases dn <;> cases dm <;> simp [FinInt.toUint, h']
<;> sorry_arith
case h_2 r h =>
have h': r.toUint = n'.toUint + m'.toUint - 2^sz := by
rw [←ih n' m']
simp [h, Int.add_comm, toSint]
simp at h'
cases dn <;> cases dm <;> simp [FinInt.toUint, h', toSint]
<;> sorry_arith
|
sz : ℕ
ih : ∀ (n m : FinInt sz), toUint (addfull n m) = toUint n + toUint m
n m : FinInt (Nat.succ sz)
⊢ toUint (addfull n m) = toUint n + toUint m
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
cases n
|
n m : FinInt Nat.zero
⊢ toUint (addfull n m) = toUint n + toUint m
|
case nil
m : FinInt Nat.zero
⊢ toUint (addfull nil m) = toUint nil + toUint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
cases m
|
case nil
m : FinInt Nat.zero
⊢ toUint (addfull nil m) = toUint nil + toUint m
|
case nil.nil
⊢ toUint (addfull nil nil) = toUint nil + toUint nil
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
simp [addfull]
|
case nil.nil
⊢ toUint (addfull nil nil) = toUint nil + toUint nil
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
cases n
|
sz : ℕ
ih : ∀ (n m : FinInt sz), toUint (addfull n m) = toUint n + toUint m
n m : FinInt (Nat.succ sz)
⊢ toUint (addfull n m) = toUint n + toUint m
|
case next
n✝ : ℕ
a✝¹ : Bool
a✝ : FinInt n✝
ih : ∀ (n m : FinInt (Nat.add n✝ 0)), toUint (addfull n m) = toUint n + toUint m
m : FinInt (Nat.succ (Nat.add n✝ 0))
⊢ toUint (addfull (next a✝¹ a✝) m) = toUint (next a✝¹ a✝) + toUint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
case next sz dn n' =>
cases m; case next dm m' =>
simp [addfull]
split
case h_1 r h =>
have h': r.toUint = n'.toUint + m'.toUint := by
rw [←ih n' m']; simp [h]
simp at h'
cases dn <;> cases dm <;> simp [FinInt.toUint, h']
<;> sorry_arith
case h_2 r h =>
have h': r.toUint = n'.toUint + m'.toUint - 2^sz := by
rw [←ih n' m']
simp [h, Int.add_comm, toSint]
simp at h'
cases dn <;> cases dm <;> simp [FinInt.toUint, h', toSint]
<;> sorry_arith
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
m : FinInt (Nat.succ (Nat.add sz 0))
⊢ toUint (addfull (next dn n') m) = toUint (next dn n') + toUint m
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
cases m
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
m : FinInt (Nat.succ (Nat.add sz 0))
⊢ toUint (addfull (next dn n') m) = toUint (next dn n') + toUint m
|
case next
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
a✝¹ : Bool
a✝ : FinInt sz
⊢ toUint (addfull (next dn n') (next a✝¹ a✝)) = toUint (next dn n') + toUint (next a✝¹ a✝)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
case next dm m' =>
simp [addfull]
split
case h_1 r h =>
have h': r.toUint = n'.toUint + m'.toUint := by
rw [←ih n' m']; simp [h]
simp at h'
cases dn <;> cases dm <;> simp [FinInt.toUint, h']
<;> sorry_arith
case h_2 r h =>
have h': r.toUint = n'.toUint + m'.toUint - 2^sz := by
rw [←ih n' m']
simp [h, Int.add_comm, toSint]
simp at h'
cases dn <;> cases dm <;> simp [FinInt.toUint, h', toSint]
<;> sorry_arith
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
⊢ toUint (addfull (next dn n') (next dm m')) = toUint (next dn n') + toUint (next dm m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
simp [addfull]
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
⊢ toUint (addfull (next dn n') (next dm m')) = toUint (next dn n') + toUint (next dm m')
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
⊢ toUint
(match addfull n' m' with
| next false r => next (dn && dm) (next (dn != dm) r)
| next true r => next (dn || dm) (next (dn == dm) r)) =
toUint (next dn n') + toUint (next dm m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
split
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
⊢ toUint
(match addfull n' m' with
| next false r => next (dn && dm) (next (dn != dm) r)
| next true r => next (dn || dm) (next (dn == dm) r)) =
toUint (next dn n') + toUint (next dm m')
|
case h_1
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
m✝ : FinInt (sz + 0)
heq✝ : addfull n' m' = next false m✝
⊢ toUint (next (dn && dm) (next (dn != dm) m✝)) = toUint (next dn n') + toUint (next dm m')
case h_2
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
m✝ : FinInt (sz + 0)
heq✝ : addfull n' m' = next true m✝
⊢ toUint (next (dn || dm) (next (dn == dm) m✝)) = toUint (next dn n') + toUint (next dm m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
case h_1 r h =>
have h': r.toUint = n'.toUint + m'.toUint := by
rw [←ih n' m']; simp [h]
simp at h'
cases dn <;> cases dm <;> simp [FinInt.toUint, h']
<;> sorry_arith
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next false r
⊢ toUint (next (dn && dm) (next (dn != dm) r)) = toUint (next dn n') + toUint (next dm m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
case h_2 r h =>
have h': r.toUint = n'.toUint + m'.toUint - 2^sz := by
rw [←ih n' m']
simp [h, Int.add_comm, toSint]
simp at h'
cases dn <;> cases dm <;> simp [FinInt.toUint, h', toSint]
<;> sorry_arith
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next true r
⊢ toUint (next (dn || dm) (next (dn == dm) r)) = toUint (next dn n') + toUint (next dm m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
have h': r.toUint = n'.toUint + m'.toUint := by
rw [←ih n' m']; simp [h]
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next false r
⊢ toUint (next (dn && dm) (next (dn != dm) r)) = toUint (next dn n') + toUint (next dm m')
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next false r
h' : toUint r = toUint n' + toUint m'
⊢ toUint (next (dn && dm) (next (dn != dm) r)) = toUint (next dn n') + toUint (next dm m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
cases dn <;> cases dm <;> simp [FinInt.toUint, h']
<;> sorry_arith
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next false r
h' : toUint r = toUint n' + toUint m'
⊢ toUint (next (dn && dm) (next (dn != dm) r)) = toUint (next dn n') + toUint (next dm m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
rw [←ih n' m']
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next false r
⊢ toUint r = toUint n' + toUint m'
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next false r
⊢ toUint r = toUint (addfull n' m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
simp [h]
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next false r
⊢ toUint r = toUint (addfull n' m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
have h': r.toUint = n'.toUint + m'.toUint - 2^sz := by
rw [←ih n' m']
simp [h, Int.add_comm, toSint]
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next true r
⊢ toUint (next (dn || dm) (next (dn == dm) r)) = toUint (next dn n') + toUint (next dm m')
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next true r
h' : toUint r = toUint n' + toUint m' - 2 ^ sz
⊢ toUint (next (dn || dm) (next (dn == dm) r)) = toUint (next dn n') + toUint (next dm m')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
cases dn <;> cases dm <;> simp [FinInt.toUint, h', toSint]
<;> sorry_arith
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next true r
h' : toUint r = toUint n' + toUint m' - 2 ^ sz
⊢ toUint (next (dn || dm) (next (dn == dm) r)) = toUint (next dn n') + toUint (next dm m')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
rw [←ih n' m']
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next true r
⊢ toUint r = toUint n' + toUint m' - 2 ^ sz
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next true r
⊢ toUint r = toUint (addfull n' m') - 2 ^ sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toUint
|
[511, 11]
|
[533, 22]
|
simp [h, Int.add_comm, toSint]
|
sz : ℕ
dn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), toUint (addfull n m) = toUint n + toUint m
dm : Bool
m' : FinInt sz
n✝ : FinInt (sz + 0 + 1)
r : FinInt (sz + 0)
h : addfull n' m' = next true r
⊢ toUint r = toUint (addfull n' m') - 2 ^ sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
cases n
|
sz : ℕ
n m : FinInt (sz + 1)
⊢ 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
|
case next
sz : ℕ
m : FinInt (sz + 1)
a✝¹ : Bool
a✝ : FinInt sz
⊢ 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
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
case next bn n' =>
cases m; case next bm m' =>
cases bn <;> cases bm <;> simp [addfull]
case false.false =>
match h: addfull n' m' with
| .next br r =>
cases br <;> simp [toSint, ←FinInt.addfull_toUint, h]
case false.true =>
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint]
. simp [h']; sorry_arith
. sorry_arith
case true.false =>
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint]
. simp [h']; sorry_arith
. sorry_arith
case true.true =>
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint, h'] <;> sorry_arith
|
sz : ℕ
m : FinInt (sz + 1)
bn : Bool
n' : FinInt sz
⊢ 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
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
cases m
|
sz : ℕ
m : FinInt (sz + 1)
bn : Bool
n' : FinInt sz
⊢ 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
|
case next
sz : ℕ
bn : Bool
n' : FinInt sz
a✝¹ : Bool
a✝ : FinInt sz
⊢ 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✝)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
case next bm m' =>
cases bn <;> cases bm <;> simp [addfull]
case false.false =>
match h: addfull n' m' with
| .next br r =>
cases br <;> simp [toSint, ←FinInt.addfull_toUint, h]
case false.true =>
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint]
. simp [h']; sorry_arith
. sorry_arith
case true.false =>
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint]
. simp [h']; sorry_arith
. sorry_arith
case true.true =>
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint, h'] <;> sorry_arith
|
sz : ℕ
bn : Bool
n' : FinInt sz
bm : Bool
m' : FinInt sz
⊢ 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')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
cases bn <;> cases bm <;> simp [addfull]
|
sz : ℕ
bn : Bool
n' : FinInt sz
bm : Bool
m' : FinInt sz
⊢ 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')
|
case false.false
sz : ℕ
n' m' : FinInt sz
⊢ 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')
case false.true
sz : ℕ
n' m' : FinInt sz
⊢ 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)
case true.false
sz : ℕ
n' m' : FinInt sz
⊢ 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)
case true.true
sz : ℕ
n' m' : FinInt sz
⊢ 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')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
case false.false =>
match h: addfull n' m' with
| .next br r =>
cases br <;> simp [toSint, ←FinInt.addfull_toUint, h]
|
sz : ℕ
n' m' : FinInt sz
⊢ 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')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
case false.true =>
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint]
. simp [h']; sorry_arith
. sorry_arith
|
sz : ℕ
n' m' : FinInt sz
⊢ 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)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
case true.false =>
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint]
. simp [h']; sorry_arith
. sorry_arith
|
sz : ℕ
n' m' : FinInt sz
⊢ 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)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
case true.true =>
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint, h'] <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
⊢ 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')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
match h: addfull n' m' with
| .next br r =>
cases br <;> simp [toSint, ←FinInt.addfull_toUint, h]
|
sz : ℕ
n' m' : FinInt sz
⊢ 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')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
cases br <;> simp [toSint, ←FinInt.addfull_toUint, h]
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
⊢ 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')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint]
. simp [h']; sorry_arith
. sorry_arith
|
sz : ℕ
n' m' : FinInt sz
⊢ 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)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
have h' := FinInt.addfull_toUint n' m'
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
⊢ 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)
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (addfull n' m') = toUint n' + toUint m'
⊢ 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)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
rw [h] at h'
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (addfull n' m') = toUint n' + toUint m'
⊢ 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)
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (next br r) = toUint n' + toUint m'
⊢ 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)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
cases br <;> simp at h' <;> simp [toSint]
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (next br r) = toUint n' + toUint m'
⊢ 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)
|
case false
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next false r
h' : toUint r = toUint n' + toUint m'
⊢ 2 ^ sz + toUint r = toUint n' + (toUint m' - 2 ^ sz) + 2 ^ (sz + 1)
case true
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next true r
h' : 2 ^ sz + toUint r = toUint n' + toUint m'
⊢ toUint r = toUint n' + (toUint m' - 2 ^ sz)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
. simp [h']; sorry_arith
|
case false
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next false r
h' : toUint r = toUint n' + toUint m'
⊢ 2 ^ sz + toUint r = toUint n' + (toUint m' - 2 ^ sz) + 2 ^ (sz + 1)
case true
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next true r
h' : 2 ^ sz + toUint r = toUint n' + toUint m'
⊢ toUint r = toUint n' + (toUint m' - 2 ^ sz)
|
case true
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next true r
h' : 2 ^ sz + toUint r = toUint n' + toUint m'
⊢ toUint r = toUint n' + (toUint m' - 2 ^ sz)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
. sorry_arith
|
case true
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next true r
h' : 2 ^ sz + toUint r = toUint n' + toUint m'
⊢ toUint r = toUint n' + (toUint m' - 2 ^ sz)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint]
. simp [h']; sorry_arith
. sorry_arith
|
sz : ℕ
n' m' : FinInt sz
⊢ 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)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
have h' := FinInt.addfull_toUint n' m'
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
⊢ 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)
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (addfull n' m') = toUint n' + toUint m'
⊢ 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)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
rw [h] at h'
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (addfull n' m') = toUint n' + toUint m'
⊢ 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)
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (next br r) = toUint n' + toUint m'
⊢ 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)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
cases br <;> simp at h' <;> simp [toSint]
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (next br r) = toUint n' + toUint m'
⊢ 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)
|
case false
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next false r
h' : toUint r = toUint n' + toUint m'
⊢ 2 ^ sz + toUint r = toUint n' - 2 ^ sz + toUint m' + 2 ^ (sz + 1)
case true
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next true r
h' : 2 ^ sz + toUint r = toUint n' + toUint m'
⊢ toUint r = toUint n' - 2 ^ sz + toUint m'
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
. simp [h']; sorry_arith
|
case false
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next false r
h' : toUint r = toUint n' + toUint m'
⊢ 2 ^ sz + toUint r = toUint n' - 2 ^ sz + toUint m' + 2 ^ (sz + 1)
case true
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next true r
h' : 2 ^ sz + toUint r = toUint n' + toUint m'
⊢ toUint r = toUint n' - 2 ^ sz + toUint m'
|
case true
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next true r
h' : 2 ^ sz + toUint r = toUint n' + toUint m'
⊢ toUint r = toUint n' - 2 ^ sz + toUint m'
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
. sorry_arith
|
case true
sz : ℕ
n' m' r : FinInt sz
h : addfull n' m' = next true r
h' : 2 ^ sz + toUint r = toUint n' + toUint m'
⊢ toUint r = toUint n' - 2 ^ sz + toUint m'
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
match h: addfull n' m' with
| .next br r =>
have h' := FinInt.addfull_toUint n' m'
rw [h] at h'
cases br <;> simp at h' <;> simp [toSint, h'] <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
⊢ 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')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
have h' := FinInt.addfull_toUint n' m'
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
⊢ 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')
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (addfull n' m') = toUint n' + toUint m'
⊢ 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')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
rw [h] at h'
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (addfull n' m') = toUint n' + toUint m'
⊢ 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')
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (next br r) = toUint n' + toUint m'
⊢ 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')
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_toSint
|
[535, 1]
|
[578, 68]
|
cases br <;> simp at h' <;> simp [toSint, h'] <;> sorry_arith
|
sz : ℕ
n' m' : FinInt sz
br : Bool
r : FinInt sz
h : addfull n' m' = next br r
h' : toUint (next br r) = toUint n' + toUint m'
⊢ 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')
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_comm
|
[580, 1]
|
[585, 44]
|
induction sz <;> cases n <;> cases m <;> simp [addfull]
|
sz : ℕ
n m : FinInt sz
⊢ addfull n m = addfull m n
|
case succ.next.next
n✝ : ℕ
a✝³ : Bool
a✝² : FinInt n✝
n_ih✝ : ∀ (n m : FinInt (Nat.add n✝ 0)), addfull n m = addfull m n
a✝¹ : Bool
a✝ : FinInt n✝
⊢ (match addfull a✝² a✝ with
| next false r => next (a✝³ && a✝¹) (next (a✝³ != a✝¹) r)
| next true r => next (a✝³ || a✝¹) (next (a✝³ == a✝¹) r)) =
match addfull a✝ a✝² with
| next false r => next (a✝¹ && a✝³) (next (a✝¹ != a✝³) r)
| next true r => next (a✝¹ || a✝³) (next (a✝¹ == a✝³) r)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_comm
|
[580, 1]
|
[585, 44]
|
case succ.next.next sz bn n' ih bm m' =>
simp [ih n' m']
split <;> cases bn <;> cases bm <;> rfl
|
sz : ℕ
bn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), addfull n m = addfull m n
bm : Bool
m' : FinInt sz
⊢ (match addfull n' m' with
| next false r => next (bn && bm) (next (bn != bm) r)
| next true r => next (bn || bm) (next (bn == bm) r)) =
match addfull m' n' with
| next false r => next (bm && bn) (next (bm != bn) r)
| next true r => next (bm || bn) (next (bm == bn) r)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_comm
|
[580, 1]
|
[585, 44]
|
simp [ih n' m']
|
sz : ℕ
bn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), addfull n m = addfull m n
bm : Bool
m' : FinInt sz
⊢ (match addfull n' m' with
| next false r => next (bn && bm) (next (bn != bm) r)
| next true r => next (bn || bm) (next (bn == bm) r)) =
match addfull m' n' with
| next false r => next (bm && bn) (next (bm != bn) r)
| next true r => next (bm || bn) (next (bm == bn) r)
|
sz : ℕ
bn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), addfull n m = addfull m n
bm : Bool
m' : FinInt sz
⊢ (match addfull m' n' with
| next false r => next (bn && bm) (next (bn != bm) r)
| next true r => next (bn || bm) (next (bn == bm) r)) =
match addfull m' n' with
| next false r => next (bm && bn) (next (bm != bn) r)
| next true r => next (bm || bn) (next (bm == bn) r)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addfull_comm
|
[580, 1]
|
[585, 44]
|
split <;> cases bn <;> cases bm <;> rfl
|
sz : ℕ
bn : Bool
n' : FinInt sz
ih : ∀ (n m : FinInt (Nat.add sz 0)), addfull n m = addfull m n
bm : Bool
m' : FinInt sz
⊢ (match addfull m' n' with
| next false r => next (bn && bm) (next (bn != bm) r)
| next true r => next (bn || bm) (next (bn == bm) r)) =
match addfull m' n' with
| next false r => next (bm && bn) (next (bm != bn) r)
| next true r => next (bm || bn) (next (bm == bn) r)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.addc_comm
|
[595, 1]
|
[596, 28]
|
simp [addc, addfull_comm]
|
sz : ℕ
n m : FinInt sz
⊢ addc n m = addc m n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_comm'
|
[602, 1]
|
[603, 27]
|
simp [add, addfull_comm]
|
sz : ℕ
n m : FinInt sz
⊢ add n m = add m n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_comm
|
[608, 1]
|
[609, 30]
|
simp [HAdd.hAdd, add_comm']
|
sz : ℕ
n m : FinInt sz
⊢ n + m = m + n
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_msb
|
[611, 11]
|
[624, 18]
|
match h: addfull n m with
| .next br r =>
have h₁ := FinInt.addfull_toUint n m
rw [h] at h₁
have h₂: n+m = r := by simp [HAdd.hAdd, add, h]
cases br <;> simp [h₂] at *
. exact h₁
. sorry_arith
|
sz : ℕ
n m : FinInt sz
⊢ toUint (n + m) =
match addfull n m with
| next false a => toUint n + toUint m
| next true a => toUint n + toUint m - 2 ^ sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_msb
|
[611, 11]
|
[624, 18]
|
have h₁ := FinInt.addfull_toUint n m
|
sz : ℕ
n m : FinInt sz
br : Bool
r : FinInt sz
h : addfull n m = next br r
⊢ toUint (n + m) =
match next br r with
| next false a => toUint n + toUint m
| next true a => toUint n + toUint m - 2 ^ sz
|
sz : ℕ
n m : FinInt sz
br : Bool
r : FinInt sz
h : addfull n m = next br r
h₁ : toUint (addfull n m) = toUint n + toUint m
⊢ toUint (n + m) =
match next br r with
| next false a => toUint n + toUint m
| next true a => toUint n + toUint m - 2 ^ sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_msb
|
[611, 11]
|
[624, 18]
|
rw [h] at h₁
|
sz : ℕ
n m : FinInt sz
br : Bool
r : FinInt sz
h : addfull n m = next br r
h₁ : toUint (addfull n m) = toUint n + toUint m
⊢ toUint (n + m) =
match next br r with
| next false a => toUint n + toUint m
| next true a => toUint n + toUint m - 2 ^ sz
|
sz : ℕ
n m : FinInt sz
br : Bool
r : FinInt sz
h : addfull n m = next br r
h₁ : toUint (next br r) = toUint n + toUint m
⊢ toUint (n + m) =
match next br r with
| next false a => toUint n + toUint m
| next true a => toUint n + toUint m - 2 ^ sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_msb
|
[611, 11]
|
[624, 18]
|
have h₂: n+m = r := by simp [HAdd.hAdd, add, h]
|
sz : ℕ
n m : FinInt sz
br : Bool
r : FinInt sz
h : addfull n m = next br r
h₁ : toUint (next br r) = toUint n + toUint m
⊢ toUint (n + m) =
match next br r with
| next false a => toUint n + toUint m
| next true a => toUint n + toUint m - 2 ^ sz
|
sz : ℕ
n m : FinInt sz
br : Bool
r : FinInt sz
h : addfull n m = next br r
h₁ : toUint (next br r) = toUint n + toUint m
h₂ : n + m = r
⊢ toUint (n + m) =
match next br r with
| next false a => toUint n + toUint m
| next true a => toUint n + toUint m - 2 ^ sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_msb
|
[611, 11]
|
[624, 18]
|
cases br <;> simp [h₂] at *
|
sz : ℕ
n m : FinInt sz
br : Bool
r : FinInt sz
h : addfull n m = next br r
h₁ : toUint (next br r) = toUint n + toUint m
h₂ : n + m = r
⊢ toUint (n + m) =
match next br r with
| next false a => toUint n + toUint m
| next true a => toUint n + toUint m - 2 ^ sz
|
case false
sz : ℕ
n m r : FinInt sz
h : addfull n m = next false r
h₁ : toUint r = toUint n + toUint m
h₂ : True
⊢ toUint r = toUint n + toUint m
case true
sz : ℕ
n m r : FinInt sz
h : addfull n m = next true r
h₂ : True
h₁ : 2 ^ sz + toUint r = toUint n + toUint m
⊢ toUint r = toUint n + toUint m - 2 ^ sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_msb
|
[611, 11]
|
[624, 18]
|
. exact h₁
|
case false
sz : ℕ
n m r : FinInt sz
h : addfull n m = next false r
h₁ : toUint r = toUint n + toUint m
h₂ : True
⊢ toUint r = toUint n + toUint m
case true
sz : ℕ
n m r : FinInt sz
h : addfull n m = next true r
h₂ : True
h₁ : 2 ^ sz + toUint r = toUint n + toUint m
⊢ toUint r = toUint n + toUint m - 2 ^ sz
|
case true
sz : ℕ
n m r : FinInt sz
h : addfull n m = next true r
h₂ : True
h₁ : 2 ^ sz + toUint r = toUint n + toUint m
⊢ toUint r = toUint n + toUint m - 2 ^ sz
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_msb
|
[611, 11]
|
[624, 18]
|
. sorry_arith
|
case true
sz : ℕ
n m r : FinInt sz
h : addfull n m = next true r
h₂ : True
h₁ : 2 ^ sz + toUint r = toUint n + toUint m
⊢ toUint r = toUint n + toUint m - 2 ^ sz
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_msb
|
[611, 11]
|
[624, 18]
|
simp [HAdd.hAdd, add, h]
|
sz : ℕ
n m : FinInt sz
br : Bool
r : FinInt sz
h : addfull n m = next br r
h₁ : toUint (next br r) = toUint n + toUint m
⊢ n + m = r
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_by_lt
|
[626, 1]
|
[638, 18]
|
intros h_bound
|
sz : ℕ
n m : FinInt sz
⊢ toUint n + toUint m < 2 ^ sz → toUint (n + m) = toUint n + toUint m
|
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
⊢ toUint (n + m) = toUint n + toUint m
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_by_lt
|
[626, 1]
|
[638, 18]
|
simp [HAdd.hAdd, FinInt.add, FinInt.addfull_toUint]
|
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
⊢ toUint (n + m) = toUint n + toUint m
|
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
⊢ toUint
(match addfull n m with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_by_lt
|
[626, 1]
|
[638, 18]
|
cases h₁: addfull n m
|
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
⊢ toUint
(match addfull n m with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
case next
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
a✝¹ : Bool
a✝ : FinInt sz
h₁ : addfull n m = next a✝¹ a✝
⊢ toUint
(match next a✝¹ a✝ with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_by_lt
|
[626, 1]
|
[638, 18]
|
case next carry r =>
have h₂: (addfull n m).toUint = (next carry r).toUint := by simp [h₁]
cases carry <;> simp at h₂
. simp [←h₂, FinInt.addfull_toUint, HAdd.hAdd]
. simp [FinInt.addfull_toUint] at h₂
rw [h₂] at h_bound
sorry_arith
|
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
carry : Bool
r : FinInt sz
h₁ : addfull n m = next carry r
⊢ toUint
(match next carry r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_by_lt
|
[626, 1]
|
[638, 18]
|
have h₂: (addfull n m).toUint = (next carry r).toUint := by simp [h₁]
|
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
carry : Bool
r : FinInt sz
h₁ : addfull n m = next carry r
⊢ toUint
(match next carry r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
carry : Bool
r : FinInt sz
h₁ : addfull n m = next carry r
h₂ : toUint (addfull n m) = toUint (next carry r)
⊢ toUint
(match next carry r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_by_lt
|
[626, 1]
|
[638, 18]
|
cases carry <;> simp at h₂
|
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
carry : Bool
r : FinInt sz
h₁ : addfull n m = next carry r
h₂ : toUint (addfull n m) = toUint (next carry r)
⊢ toUint
(match next carry r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
case false
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
r : FinInt sz
h₁ : addfull n m = next false r
h₂ : toUint (addfull n m) = toUint r
⊢ toUint
(match next false r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
case true
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
r : FinInt sz
h₁ : addfull n m = next true r
h₂ : toUint (addfull n m) = 2 ^ sz + toUint r
⊢ toUint
(match next true r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_by_lt
|
[626, 1]
|
[638, 18]
|
. simp [←h₂, FinInt.addfull_toUint, HAdd.hAdd]
|
case false
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
r : FinInt sz
h₁ : addfull n m = next false r
h₂ : toUint (addfull n m) = toUint r
⊢ toUint
(match next false r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
case true
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
r : FinInt sz
h₁ : addfull n m = next true r
h₂ : toUint (addfull n m) = 2 ^ sz + toUint r
⊢ toUint
(match next true r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
case true
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
r : FinInt sz
h₁ : addfull n m = next true r
h₂ : toUint (addfull n m) = 2 ^ sz + toUint r
⊢ toUint
(match next true r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_by_lt
|
[626, 1]
|
[638, 18]
|
. simp [FinInt.addfull_toUint] at h₂
rw [h₂] at h_bound
sorry_arith
|
case true
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
r : FinInt sz
h₁ : addfull n m = next true r
h₂ : toUint (addfull n m) = 2 ^ sz + toUint r
⊢ toUint
(match next true r with
| next carry n => n) =
Add.add (toUint n) (toUint m)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_by_lt
|
[626, 1]
|
[638, 18]
|
simp [h₁]
|
sz : ℕ
n m : FinInt sz
h_bound : toUint n + toUint m < 2 ^ sz
carry : Bool
r : FinInt sz
h₁ : addfull n m = next carry r
⊢ toUint (addfull n m) = toUint (next carry r)
|
no goals
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_rem
|
[640, 1]
|
[652, 52]
|
simp [FinInt.add_toUint_msb]
|
sz : ℕ
n m : FinInt sz
⊢ toUint (n + m) = if toUint n + toUint m < 2 ^ sz then toUint n + toUint m else toUint n + toUint m - 2 ^ sz
|
sz : ℕ
n m : FinInt sz
⊢ (match addfull n m 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
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_rem
|
[640, 1]
|
[652, 52]
|
cases h_full: addfull n m
|
sz : ℕ
n m : FinInt sz
⊢ (match addfull n m 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 next
sz : ℕ
n m : FinInt sz
a✝¹ : Bool
a✝ : FinInt sz
h_full : addfull n m = next a✝¹ a✝
⊢ (match next a✝¹ a✝ 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
|
https://github.com/opencompl/lean-mlir.git
|
e43d21592801e5e40477b14b7a554e356060c40c
|
MLIR/Util/FinInt.lean
|
FinInt.add_toUint_rem
|
[640, 1]
|
[652, 52]
|
case next br r' =>
cases br <;> simp
. have h := O_lt r'; rw [←h_full] at h
simp [FinInt.addfull_toUint] at h; simp [h]
. have h := I_not_lt r'; rw [←h_full] at h; sorry
|
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
|
no goals
|
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