Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files Community
1
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.mod2_fequal
[70, 1]
[71, 21]
intros h
x y : ℤ n : ℕ ⊢ x = y → mod2 x n = mod2 y n
x y : ℤ n : ℕ h : x = y ⊢ mod2 x n = mod2 y n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_fequal
[70, 1]
[71, 21]
simp [h]
x y : ℤ n : ℕ h : x = y ⊢ mod2 x n = mod2 y n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_zero
[73, 1]
[75, 23]
simp [mod2]
n : ℕ ⊢ mod2 0 n = 0
n : ℕ ⊢ 2 ^ n % 2 ^ n = 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_zero
[73, 1]
[75, 23]
simp [Int.emod_self]
n : ℕ ⊢ 2 ^ n % 2 ^ n = 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_exp_n
[77, 1]
[80, 23]
simp [mod2]
n : ℕ ⊢ mod2 (2 ^ n) n = 0
n : ℕ ⊢ 2 ^ n % 2 ^ n = 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_exp_n
[77, 1]
[80, 23]
simp [Int.emod_self]
n : ℕ ⊢ 2 ^ n % 2 ^ n = 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_add_left
[83, 1]
[84, 8]
sorry
n : ℕ x : ℤ ⊢ mod2 (2 ^ n + x) n = mod2 x n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_add_right
[86, 1]
[87, 8]
sorry
x : ℤ n : ℕ ⊢ mod2 (x + 2 ^ n) n = mod2 x n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_ge
[94, 1]
[97, 66]
simp [smod2]
a : ℤ n : ℕ ⊢ smod2 a n ≥ -2 ^ n
a : ℤ n : ℕ ⊢ -2 ^ n ≤ if 2 ^ n ≤ mod2 a (n + 1) then mod2 a (n + 1) - 2 ^ (n + 1) else mod2 a (n + 1)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_ge
[94, 1]
[97, 66]
split
a : ℤ n : ℕ ⊢ -2 ^ n ≤ if 2 ^ n ≤ mod2 a (n + 1) then mod2 a (n + 1) - 2 ^ (n + 1) else mod2 a (n + 1)
case inl a : ℤ n : ℕ h✝ : 2 ^ n ≤ mod2 a (n + 1) ⊢ -2 ^ n ≤ mod2 a (n + 1) - 2 ^ (n + 1) case inr a : ℤ n : ℕ h✝ : ¬2 ^ n ≤ mod2 a (n + 1) ⊢ -2 ^ n ≤ mod2 a (n + 1)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_ge
[94, 1]
[97, 66]
. sorry_arith
case inl a : ℤ n : ℕ h✝ : 2 ^ n ≤ mod2 a (n + 1) ⊢ -2 ^ n ≤ mod2 a (n + 1) - 2 ^ (n + 1) case inr a : ℤ n : ℕ h✝ : ¬2 ^ n ≤ mod2 a (n + 1) ⊢ -2 ^ n ≤ mod2 a (n + 1)
case inr a : ℤ n : ℕ h✝ : ¬2 ^ n ≤ mod2 a (n + 1) ⊢ -2 ^ n ≤ mod2 a (n + 1)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_ge
[94, 1]
[97, 66]
. apply Int.ge_trans 0 mod2_ge (Int.zero_ge_neg Int.two_pow_ge)
case inr a : ℤ n : ℕ h✝ : ¬2 ^ n ≤ mod2 a (n + 1) ⊢ -2 ^ n ≤ mod2 a (n + 1)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_lt
[99, 1]
[102, 16]
simp [smod2]
a : ℤ n : ℕ ⊢ smod2 a n < 2 ^ n
a : ℤ n : ℕ ⊢ (if 2 ^ n ≤ mod2 a (n + 1) then mod2 a (n + 1) - 2 ^ (n + 1) else mod2 a (n + 1)) < 2 ^ n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_lt
[99, 1]
[102, 16]
split
a : ℤ n : ℕ ⊢ (if 2 ^ n ≤ mod2 a (n + 1) then mod2 a (n + 1) - 2 ^ (n + 1) else mod2 a (n + 1)) < 2 ^ n
case inl a : ℤ n : ℕ h✝ : 2 ^ n ≤ mod2 a (n + 1) ⊢ mod2 a (n + 1) - 2 ^ (n + 1) < 2 ^ n case inr a : ℤ n : ℕ h✝ : ¬2 ^ n ≤ mod2 a (n + 1) ⊢ mod2 a (n + 1) < 2 ^ n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_lt
[99, 1]
[102, 16]
. sorry_arith
case inl a : ℤ n : ℕ h✝ : 2 ^ n ≤ mod2 a (n + 1) ⊢ mod2 a (n + 1) - 2 ^ (n + 1) < 2 ^ n case inr a : ℤ n : ℕ h✝ : ¬2 ^ n ≤ mod2 a (n + 1) ⊢ mod2 a (n + 1) < 2 ^ n
case inr a : ℤ n : ℕ h✝ : ¬2 ^ n ≤ mod2 a (n + 1) ⊢ mod2 a (n + 1) < 2 ^ n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_lt
[99, 1]
[102, 16]
. sorry_arith
case inr a : ℤ n : ℕ h✝ : ¬2 ^ n ≤ mod2 a (n + 1) ⊢ mod2 a (n + 1) < 2 ^ n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_idem
[107, 1]
[108, 8]
sorry
n : ℕ a : ℤ ⊢ a ≥ -2 ^ n ∧ a < 2 ^ n → smod2 a n = a
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.smod2_as_mod2
[119, 1]
[120, 8]
sorry
a : ℤ n : ℕ ⊢ smod2 a n = mod2 (a + 2 ^ n) (n + 1) - 2 ^ n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.cong2_to_eq
[143, 1]
[149, 48]
intros h ha hb
a b : ℤ n : ℕ ⊢ a ≡ b [2^n] → a ≥ 0 ∧ a < 2 ^ n → b ≥ 0 ∧ b < 2 ^ n → a = b
a b : ℤ n : ℕ h : a ≡ b [2^n] ha : a ≥ 0 ∧ a < 2 ^ n hb : b ≥ 0 ∧ b < 2 ^ n ⊢ a = b
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.cong2_to_eq
[143, 1]
[149, 48]
rw [←mod2_idem ha, ←mod2_idem hb]
a b : ℤ n : ℕ h : a ≡ b [2^n] ha : a ≥ 0 ∧ a < 2 ^ n hb : b ≥ 0 ∧ b < 2 ^ n ⊢ a = b
a b : ℤ n : ℕ h : a ≡ b [2^n] ha : a ≥ 0 ∧ a < 2 ^ n hb : b ≥ 0 ∧ b < 2 ^ n ⊢ mod2 a n = mod2 b n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.cong2_to_eq
[143, 1]
[149, 48]
assumption
a b : ℤ n : ℕ h : a ≡ b [2^n] ha : a ≥ 0 ∧ a < 2 ^ n hb : b ≥ 0 ∧ b < 2 ^ n ⊢ mod2 a n = mod2 b n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.scong2_to_eq
[151, 1]
[157, 50]
intros h ha hb
a b : ℤ n : ℕ ⊢ a ≡ b [±2^n] → a ≥ -2 ^ n ∧ a < 2 ^ n → b ≥ -2 ^ n ∧ b < 2 ^ n → a = b
a b : ℤ n : ℕ h : a ≡ b [±2^n] ha : a ≥ -2 ^ n ∧ a < 2 ^ n hb : b ≥ -2 ^ n ∧ b < 2 ^ n ⊢ a = b
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.scong2_to_eq
[151, 1]
[157, 50]
rw [←smod2_idem ha, ←smod2_idem hb]
a b : ℤ n : ℕ h : a ≡ b [±2^n] ha : a ≥ -2 ^ n ∧ a < 2 ^ n hb : b ≥ -2 ^ n ∧ b < 2 ^ n ⊢ a = b
a b : ℤ n : ℕ h : a ≡ b [±2^n] ha : a ≥ -2 ^ n ∧ a < 2 ^ n hb : b ≥ -2 ^ n ∧ b < 2 ^ n ⊢ smod2 a n = smod2 b n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.scong2_to_eq
[151, 1]
[157, 50]
assumption
a b : ℤ n : ℕ h : a ≡ b [±2^n] ha : a ≥ -2 ^ n ∧ a < 2 ^ n hb : b ≥ -2 ^ n ∧ b < 2 ^ n ⊢ smod2 a n = smod2 b n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_add_l
[160, 1]
[161, 8]
sorry
a : ℤ n : ℕ b : ℤ ⊢ mod2 (mod2 a n + b) n = mod2 (a + b) n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_add_r
[164, 1]
[165, 8]
sorry
a b : ℤ n : ℕ ⊢ mod2 (a + mod2 b n) n = mod2 (a + b) n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_neg
[168, 1]
[169, 8]
sorry
a : ℤ n : ℕ ⊢ mod2 (-mod2 a n) n = mod2 (-a) n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_sub_r
[172, 1]
[173, 8]
sorry
a b : ℤ n : ℕ ⊢ mod2 (a - mod2 b n) n = mod2 (a - b) n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_sub_l
[176, 1]
[177, 8]
sorry
a : ℤ n : ℕ b : ℤ ⊢ mod2 (mod2 a n - b) n = mod2 (a - b) n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.cong2_mod2_right
[179, 1]
[180, 39]
simp [cong2, mod2_idem mod2_bounds]
n : ℕ a b : ℤ ⊢ a ≡ b [2^n] → a ≡ mod2 b n [2^n]
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.cong2_mod2_left
[182, 1]
[183, 39]
simp [cong2, mod2_idem mod2_bounds]
n : ℕ a b : ℤ ⊢ a ≡ b [2^n] → mod2 a n ≡ b [2^n]
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ge
[276, 1]
[280, 67]
revert n
sz : ℕ n : FinInt sz ⊢ toUint n ≥ 0
sz : ℕ ⊢ ∀ {n : FinInt sz}, toUint n ≥ 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ge
[276, 1]
[280, 67]
induction sz <;> intros n <;> cases n <;> simp
sz : ℕ ⊢ ∀ {n : FinInt sz}, toUint n ≥ 0
case succ.next n✝ : ℕ a✝¹ : Bool a✝ : FinInt n✝ n_ih✝ : ∀ {n : FinInt (Nat.add n✝ 0)}, toUint n ≥ 0 ⊢ 0 ≤ toUint (next a✝¹ a✝)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ge
[276, 1]
[280, 67]
case next sz bn n' ih => cases bn <;> simp [@ih n'] apply Int.add_ge_zero; apply Int.pow_ge_zero; decide; apply ih
sz : ℕ bn : Bool n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ 0 ≤ toUint (next bn n')
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ge
[276, 1]
[280, 67]
cases bn <;> simp [@ih n']
sz : ℕ bn : Bool n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ 0 ≤ toUint (next bn n')
case true sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ 0 ≤ 2 ^ sz + toUint n'
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ge
[276, 1]
[280, 67]
apply Int.add_ge_zero
case true sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ 0 ≤ 2 ^ sz + toUint n'
case true.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ 2 ^ sz ≥ 0 case true.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ toUint n' ≥ 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ge
[276, 1]
[280, 67]
apply Int.pow_ge_zero
case true.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ 2 ^ sz ≥ 0 case true.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ toUint n' ≥ 0
case true.a.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ 2 ≥ 0 case true.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ toUint n' ≥ 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ge
[276, 1]
[280, 67]
decide
case true.a.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ 2 ≥ 0 case true.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ toUint n' ≥ 0
case true.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ toUint n' ≥ 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ge
[276, 1]
[280, 67]
apply ih
case true.a sz : ℕ n' : FinInt sz ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0 ⊢ toUint n' ≥ 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_lt
[282, 1]
[284, 8]
revert n
sz : ℕ n : FinInt sz ⊢ toUint n < 2 ^ sz
sz : ℕ ⊢ ∀ {n : FinInt sz}, toUint n < 2 ^ sz
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_lt
[282, 1]
[284, 8]
induction sz <;> intros n <;> cases n <;> simp
sz : ℕ ⊢ ∀ {n : FinInt sz}, toUint n < 2 ^ sz
case succ.next n✝ : ℕ a✝¹ : Bool a✝ : FinInt n✝ n_ih✝ : ∀ {n : FinInt (Nat.add n✝ 0)}, toUint n < 2 ^ Nat.add n✝ 0 ⊢ toUint (next a✝¹ a✝) < 2 ^ Nat.succ n✝
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_lt
[282, 1]
[284, 8]
sorry
case succ.next n✝ : ℕ a✝¹ : Bool a✝ : FinInt n✝ n_ih✝ : ∀ {n : FinInt (Nat.add n✝ 0)}, toUint n < 2 ^ Nat.add n✝ 0 ⊢ toUint (next a✝¹ a✝) < 2 ^ Nat.succ n✝
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_ge
[303, 1]
[304, 8]
sorry
sz : ℕ n : FinInt (sz + 1) ⊢ toSint n ≥ -2 ^ sz
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_lt
[312, 1]
[316, 16]
cases n
sz : ℕ n : FinInt (sz + 1) ⊢ toSint n < 2 ^ sz
case next sz : ℕ a✝¹ : Bool a✝ : FinInt sz ⊢ toSint (next a✝¹ a✝) < 2 ^ sz
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_lt
[312, 1]
[316, 16]
case next bn n' => cases bn <;> simp [toSint] . apply toUint_lt . sorry_arith
sz : ℕ bn : Bool n' : FinInt sz ⊢ toSint (next bn n') < 2 ^ sz
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_lt
[312, 1]
[316, 16]
cases bn <;> simp [toSint]
sz : ℕ bn : Bool n' : FinInt sz ⊢ toSint (next bn n') < 2 ^ sz
case false sz : ℕ n' : FinInt sz ⊢ toUint n' < 2 ^ sz case true sz : ℕ n' : FinInt sz ⊢ toUint n' - 2 ^ sz < 2 ^ sz
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_lt
[312, 1]
[316, 16]
. apply toUint_lt
case false sz : ℕ n' : FinInt sz ⊢ toUint n' < 2 ^ sz case true sz : ℕ n' : FinInt sz ⊢ toUint n' - 2 ^ sz < 2 ^ sz
case true sz : ℕ n' : FinInt sz ⊢ toUint n' - 2 ^ sz < 2 ^ sz
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_lt
[312, 1]
[316, 16]
. sorry_arith
case true sz : ℕ n' : FinInt sz ⊢ toUint n' - 2 ^ sz < 2 ^ sz
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_zero
[325, 1]
[329, 35]
induction sz with | zero => decide | succ n ih => simp [toUint, ih]
sz : ℕ ⊢ toUint zero = 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_zero
[325, 1]
[329, 35]
decide
case zero ⊢ toUint zero = 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_zero
[325, 1]
[329, 35]
simp [toUint, ih]
case succ n : ℕ ih : toUint zero = 0 ⊢ toUint zero = 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_one
[331, 1]
[336, 70]
intros h
sz : ℕ ⊢ sz > 0 → toUint one = 1
sz : ℕ h : sz > 0 ⊢ toUint one = 1
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_one
[331, 1]
[336, 70]
induction sz with | zero => cases (by decide: ¬ 0 > 0) h | succ n ih => cases n; decide; simp [toUint]; apply ih; simp_arith
sz : ℕ h : sz > 0 ⊢ toUint one = 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_one
[331, 1]
[336, 70]
cases (by decide: ¬ 0 > 0) h
case zero h : Nat.zero > 0 ⊢ toUint one = 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_one
[331, 1]
[336, 70]
decide
h : Nat.zero > 0 ⊢ ¬0 > 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_one
[331, 1]
[336, 70]
cases n
case succ n : ℕ ih : n > 0 → toUint one = 1 h : Nat.succ n > 0 ⊢ toUint one = 1
case succ.zero ih : Nat.zero > 0 → toUint one = 1 h : Nat.succ Nat.zero > 0 ⊢ toUint one = 1 case succ.succ n✝ : ℕ ih : Nat.succ n✝ > 0 → toUint one = 1 h : Nat.succ (Nat.succ n✝) > 0 ⊢ toUint one = 1
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_one
[331, 1]
[336, 70]
decide
case succ.zero ih : Nat.zero > 0 → toUint one = 1 h : Nat.succ Nat.zero > 0 ⊢ toUint one = 1 case succ.succ n✝ : ℕ ih : Nat.succ n✝ > 0 → toUint one = 1 h : Nat.succ (Nat.succ n✝) > 0 ⊢ toUint one = 1
case succ.succ n✝ : ℕ ih : Nat.succ n✝ > 0 → toUint one = 1 h : Nat.succ (Nat.succ n✝) > 0 ⊢ toUint one = 1
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_one
[331, 1]
[336, 70]
apply ih
case succ.succ n✝ : ℕ ih : Nat.succ n✝ > 0 → toUint one = 1 h : Nat.succ (Nat.succ n✝) > 0 ⊢ toUint one = 1
case succ.succ n✝ : ℕ ih : Nat.succ n✝ > 0 → toUint one = 1 h : Nat.succ (Nat.succ n✝) > 0 ⊢ Nat.succ n✝ > 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_one
[331, 1]
[336, 70]
simp_arith
case succ.succ n✝ : ℕ ih : Nat.succ n✝ > 0 → toUint one = 1 h : Nat.succ (Nat.succ n✝) > 0 ⊢ Nat.succ n✝ > 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_minusOne
[338, 1]
[342, 48]
induction sz with | zero => decide | succ n ih => simp [toUint, ih]; sorry_arith
sz : ℕ ⊢ toUint minusOne = 2 ^ sz - 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_minusOne
[338, 1]
[342, 48]
decide
case zero ⊢ toUint minusOne = 2 ^ Nat.zero - 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_minusOne
[338, 1]
[342, 48]
simp [toUint, ih]
case succ n : ℕ ih : toUint minusOne = 2 ^ n - 1 ⊢ toUint minusOne = 2 ^ Nat.succ n - 1
case succ n : ℕ ih : toUint minusOne = 2 ^ n - 1 ⊢ 2 ^ n + (2 ^ n - 1) = 2 ^ Nat.succ n - 1
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_minusOne
[338, 1]
[342, 48]
sorry_arith
case succ n : ℕ ih : toUint minusOne = 2 ^ n - 1 ⊢ 2 ^ n + (2 ^ n - 1) = 2 ^ Nat.succ n - 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.msb_bound
[348, 1]
[350, 8]
sorry
sz : ℕ b : Bool n : FinInt sz ⊢ toUint (next b n) < 2 ^ sz ↔ b = false
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_of_toUint
[386, 1]
[393, 47]
match n with | .O m => simp [toSint, toUint] | .I m => simp [toSint, toUint]; sorry_arith
sz : ℕ n : FinInt (sz + 1) ⊢ toSint n = match n with | next false a => toUint n | next true a => toUint n - 2 ^ (sz + 1)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_of_toUint
[386, 1]
[393, 47]
simp [toSint, toUint]
sz : ℕ n : FinInt (sz + 1) m : FinInt sz ⊢ toSint (O m) = match O m with | next false a => toUint (O m) | next true a => toUint (O m) - 2 ^ (sz + 1)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_of_toUint
[386, 1]
[393, 47]
simp [toSint, toUint]
sz : ℕ n : FinInt (sz + 1) m : FinInt sz ⊢ toSint (I m) = match I m with | next false a => toUint (I m) | next true a => toUint (I m) - 2 ^ (sz + 1)
sz : ℕ n : FinInt (sz + 1) m : FinInt sz ⊢ toUint m - 2 ^ sz = 2 ^ sz + toUint m - 2 ^ (sz + 1)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_of_toUint
[386, 1]
[393, 47]
sorry_arith
sz : ℕ n : FinInt (sz + 1) m : FinInt sz ⊢ toUint m - 2 ^ sz = 2 ^ sz + toUint m - 2 ^ (sz + 1)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_of_toSint
[395, 1]
[402, 47]
match n with | .O m => simp [toSint, toUint] | .I m => simp [toSint, toUint]; sorry_arith
sz : ℕ n : FinInt (sz + 1) ⊢ toUint n = match n with | next false a => toSint n | next true a => toSint n + 2 ^ (sz + 1)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_of_toSint
[395, 1]
[402, 47]
simp [toSint, toUint]
sz : ℕ n : FinInt (sz + 1) m : FinInt sz ⊢ toUint (O m) = match O m with | next false a => toSint (O m) | next true a => toSint (O m) + 2 ^ (sz + 1)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_of_toSint
[395, 1]
[402, 47]
simp [toSint, toUint]
sz : ℕ n : FinInt (sz + 1) m : FinInt sz ⊢ toUint (I m) = match I m with | next false a => toSint (I m) | next true a => toSint (I m) + 2 ^ (sz + 1)
sz : ℕ n : FinInt (sz + 1) m : FinInt sz ⊢ 2 ^ sz + toUint m = toUint m - 2 ^ sz + 2 ^ (sz + 1)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_of_toSint
[395, 1]
[402, 47]
sorry_arith
sz : ℕ n : FinInt (sz + 1) m : FinInt sz ⊢ 2 ^ sz + toUint m = toUint m - 2 ^ sz + 2 ^ (sz + 1)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ofInt
[404, 1]
[410, 10]
induction sz
sz : ℕ n : ℤ ⊢ toUint (ofInt sz n) = mod2 n sz
case zero n : ℤ ⊢ toUint (ofInt Nat.zero n) = mod2 n Nat.zero case succ n : ℤ n✝ : ℕ n_ih✝ : toUint (ofInt n✝ n) = mod2 n n✝ ⊢ toUint (ofInt (Nat.succ n✝) n) = mod2 n (Nat.succ n✝)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ofInt
[404, 1]
[410, 10]
case zero => simp [mod2]; sorry_arith
n : ℤ ⊢ toUint (ofInt Nat.zero n) = mod2 n Nat.zero
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ofInt
[404, 1]
[410, 10]
case succ sz ih => sorry
n : ℤ sz : ℕ ih : toUint (ofInt sz n) = mod2 n sz ⊢ toUint (ofInt (Nat.succ sz) n) = mod2 n (Nat.succ sz)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ofInt
[404, 1]
[410, 10]
simp [mod2]
n : ℤ ⊢ toUint (ofInt Nat.zero n) = mod2 n Nat.zero
n : ℤ ⊢ 0 = n % 1
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ofInt
[404, 1]
[410, 10]
sorry_arith
n : ℤ ⊢ 0 = n % 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ofInt
[404, 1]
[410, 10]
sorry
n : ℤ sz : ℕ ih : toUint (ofInt sz n) = mod2 n sz ⊢ toUint (ofInt (Nat.succ sz) n) = mod2 n (Nat.succ sz)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toUint_ofNat
[412, 1]
[414, 35]
simp [OfNat.ofNat, toUint_ofInt]
sz n : ℕ ⊢ toUint (OfNat.ofNat n) = mod2 (↑n) sz
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.toSint_ofSint
[416, 1]
[418, 8]
sorry
sz : ℕ n : ℤ ⊢ toSint (ofInt (sz + 1) n) = smod2 n sz
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
induction sz
sz : ℕ n : ℤ ⊢ toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz
case zero n : ℤ ⊢ toUint (FinInt.ofIntAux Nat.zero n).fst = mod2 n Nat.zero ∧ (FinInt.ofIntAux Nat.zero n).snd = n / 2 ^ Nat.zero case succ n : ℤ n✝ : ℕ n_ih✝ : toUint (FinInt.ofIntAux n✝ n).fst = mod2 n n✝ ∧ (FinInt.ofIntAux n✝ n).snd = n / 2 ^ n✝ ⊢ toUint (FinInt.ofIntAux (Nat.succ n✝) n).fst = mod2 n (Nat.succ n✝) ∧ (FinInt.ofIntAux (Nat.succ n✝) n).snd = n / 2 ^ Nat.succ n✝
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
case zero => simp [FinInt.ofIntAux]; sorry_arith
n : ℤ ⊢ toUint (FinInt.ofIntAux Nat.zero n).fst = mod2 n Nat.zero ∧ (FinInt.ofIntAux Nat.zero n).snd = n / 2 ^ Nat.zero
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
case succ sz ih => simp [FinInt.ofIntAux, ih]; constructor . have h: (n / 2^sz % 2 = 0) ∨ (n / 2^sz %2 = 1) := by sorry match h with | .inl h => simp [h, ih]; sorry_arith | .inr h => simp [h, ih]; sorry_arith . sorry_arith
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ toUint (FinInt.ofIntAux (Nat.succ sz) n).fst = mod2 n (Nat.succ sz) ∧ (FinInt.ofIntAux (Nat.succ sz) n).snd = n / 2 ^ Nat.succ sz
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
simp [FinInt.ofIntAux]
n : ℤ ⊢ toUint (FinInt.ofIntAux Nat.zero n).fst = mod2 n Nat.zero ∧ (FinInt.ofIntAux Nat.zero n).snd = n / 2 ^ Nat.zero
n : ℤ ⊢ 0 = mod2 n 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
sorry_arith
n : ℤ ⊢ 0 = mod2 n 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
simp [FinInt.ofIntAux, ih]
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ toUint (FinInt.ofIntAux (Nat.succ sz) n).fst = mod2 n (Nat.succ sz) ∧ (FinInt.ofIntAux (Nat.succ sz) n).snd = n / 2 ^ Nat.succ sz
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ toUint (next (n / 2 ^ sz % 2 == 1) (FinInt.ofIntAux sz n).fst) = mod2 n (Nat.succ sz) ∧ n / 2 ^ sz / 2 = n / 2 ^ Nat.succ sz
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
constructor
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ toUint (next (n / 2 ^ sz % 2 == 1) (FinInt.ofIntAux sz n).fst) = mod2 n (Nat.succ sz) ∧ n / 2 ^ sz / 2 = n / 2 ^ Nat.succ sz
case left n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ toUint (next (n / 2 ^ sz % 2 == 1) (FinInt.ofIntAux sz n).fst) = mod2 n (Nat.succ sz) case right n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ n / 2 ^ sz / 2 = n / 2 ^ Nat.succ sz
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
. have h: (n / 2^sz % 2 = 0) ∨ (n / 2^sz %2 = 1) := by sorry match h with | .inl h => simp [h, ih]; sorry_arith | .inr h => simp [h, ih]; sorry_arith
case left n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ toUint (next (n / 2 ^ sz % 2 == 1) (FinInt.ofIntAux sz n).fst) = mod2 n (Nat.succ sz) case right n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ n / 2 ^ sz / 2 = n / 2 ^ Nat.succ sz
case right n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ n / 2 ^ sz / 2 = n / 2 ^ Nat.succ sz
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
. sorry_arith
case right n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ n / 2 ^ sz / 2 = n / 2 ^ Nat.succ sz
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
sorry
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz ⊢ n / 2 ^ sz % 2 = 0 ∨ n / 2 ^ sz % 2 = 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
simp [h, ih]
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz h✝ : n / 2 ^ sz % 2 = 0 ∨ n / 2 ^ sz % 2 = 1 h : n / 2 ^ sz % 2 = 0 ⊢ toUint (next (n / 2 ^ sz % 2 == 1) (FinInt.ofIntAux sz n).fst) = mod2 n (Nat.succ sz)
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz h✝ : n / 2 ^ sz % 2 = 0 ∨ n / 2 ^ sz % 2 = 1 h : n / 2 ^ sz % 2 = 0 ⊢ mod2 n sz = mod2 n (Nat.succ sz)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
sorry_arith
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz h✝ : n / 2 ^ sz % 2 = 0 ∨ n / 2 ^ sz % 2 = 1 h : n / 2 ^ sz % 2 = 0 ⊢ mod2 n sz = mod2 n (Nat.succ sz)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
simp [h, ih]
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz h✝ : n / 2 ^ sz % 2 = 0 ∨ n / 2 ^ sz % 2 = 1 h : n / 2 ^ sz % 2 = 1 ⊢ toUint (next (n / 2 ^ sz % 2 == 1) (FinInt.ofIntAux sz n).fst) = mod2 n (Nat.succ sz)
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz h✝ : n / 2 ^ sz % 2 = 0 ∨ n / 2 ^ sz % 2 = 1 h : n / 2 ^ sz % 2 = 1 ⊢ 2 ^ sz + mod2 n sz = mod2 n (Nat.succ sz)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.ofIntAux_spec
[420, 1]
[432, 18]
sorry_arith
n : ℤ sz : ℕ ih : toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz h✝ : n / 2 ^ sz % 2 = 0 ∨ n / 2 ^ sz % 2 = 1 h : n / 2 ^ sz % 2 = 1 ⊢ 2 ^ sz + mod2 n sz = mod2 n (Nat.succ sz)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.eq_of_toUint_eq
[434, 1]
[446, 28]
intros h <;> induction sz
sz : ℕ a b : FinInt sz ⊢ toUint a = toUint b → a = b
case zero a b : FinInt Nat.zero h : toUint a = toUint b ⊢ a = b case succ n✝ : ℕ n_ih✝ : ∀ (a b : FinInt n✝), toUint a = toUint b → a = b a b : FinInt (Nat.succ n✝) 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]
case zero => cases a; cases b; rfl
a b : FinInt Nat.zero 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_eq
[434, 1]
[446, 28]
case succ sz ih => cases a; 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 ih : ∀ (a b : FinInt sz), toUint a = toUint b → a = b a b : FinInt (Nat.succ 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_eq
[434, 1]
[446, 28]
cases a
a b : FinInt Nat.zero h : toUint a = toUint b ⊢ a = b
case nil b : FinInt Nat.zero h : toUint nil = toUint b ⊢ nil = b
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.eq_of_toUint_eq
[434, 1]
[446, 28]
cases b
case nil b : FinInt Nat.zero h : toUint nil = toUint b ⊢ nil = b
case nil.nil h : toUint nil = toUint nil ⊢ nil = nil
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.eq_of_toUint_eq
[434, 1]
[446, 28]
rfl
case nil.nil h : toUint nil = toUint nil ⊢ nil = nil
no goals