Datasets:
internlm
/
Lean-Github

Dataset card Data Studio Files
xet
 Community
1
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stringclasses
147 values
commit
stringclasses
147 values
file_path
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7
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state_after
stringlengths
6
2.09M
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mul_two
[39, 1]
[44, 22]
rw [h]
n : ℤ h : 2 = 1 + 1 ⊢ n * 2 = n + n
n : ℤ h : 2 = 1 + 1 ⊢ n * (1 + 1) = n + n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mul_two
[39, 1]
[44, 22]
rw [Int.mul_add]
n : ℤ h : 2 = 1 + 1 ⊢ n * (1 + 1) = n + n
n : ℤ h : 2 = 1 + 1 ⊢ n * 1 + n * 1 = n + n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mul_two
[39, 1]
[44, 22]
simp [Int.mul_one]
n : ℤ h : 2 = 1 + 1 ⊢ n * 1 + n * 1 = n + n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_zero
[48, 1]
[48, 45]
rfl
n : ℤ ⊢ n ^ 0 = 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_succ
[50, 1]
[50, 64]
rfl
n : ℤ m : ℕ ⊢ n ^ (m + 1) = n ^ m * n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.two_pow_ge
[52, 1]
[53, 8]
sorry
n : ℕ ⊢ 2 ^ n ≥ 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.two_pow_pos
[55, 1]
[56, 8]
sorry
n : ℕ ⊢ 2 ^ n > 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.one_le_two_pow
[58, 1]
[59, 8]
sorry
n : ℕ ⊢ 1 ≤ 2 ^ n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.one_lt_two_pow
[61, 1]
[62, 8]
sorry
n : ℕ ⊢ n > 0 → 1 < 2 ^ n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mod_bounds
[64, 1]
[65, 8]
sorry
a b : ℤ ⊢ a ≥ 0 → a < b → a % b = a
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mod_mod
[67, 1]
[68, 8]
sorry
a b : ℤ ⊢ a % b % b = a % b
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mod_ge_neg
[70, 1]
[71, 8]
sorry
a b : ℤ ⊢ a % b ≥ -b
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mod_ge
[73, 1]
[74, 8]
sorry
a b : ℤ ⊢ a ≥ 0 → a % b ≥ 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mod_lt
[76, 1]
[77, 8]
sorry
a b : ℤ ⊢ b > 0 → a % b < b
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.add_mod_right
[79, 1]
[80, 8]
sorry
x z : ℤ ⊢ z > 0 → x ≥ 0 → (x + z) % z = x % z
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.add_mod_left
[82, 1]
[83, 8]
sorry
x z : ℤ ⊢ z > 0 → x ≥ 0 → (z + x) % z = x % z
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.ge_zero_eq_nonneg
[90, 1]
[91, 30]
simp [GE.ge, LE.le, Int.le]
n : ℤ ⊢ n ≥ 0 ↔ NonNeg n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.zero_ge_neg
[93, 1]
[94, 43]
simp [GE.ge, LE.le, Int.le, Int.neg_neg]
n : ℤ ⊢ n ≥ 0 → 0 ≥ -n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.add_ge_zero
[98, 1]
[98, 70]
sorry
n m : ℤ ⊢ n ≥ 0 → m ≥ 0 → n + m ≥ 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.le_succ
[105, 1]
[107, 14]
suffices NonNeg 1 by simp [LE.le, Int.le, add_sub_assoc, add_sub]; trivial
n : ℤ ⊢ n ≤ n + 1
n : ℤ ⊢ NonNeg 1
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.le_succ
[105, 1]
[107, 14]
constructor
n : ℤ ⊢ NonNeg 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.le_succ
[105, 1]
[107, 14]
simp [LE.le, Int.le, add_sub_assoc, add_sub]
n : ℤ this : NonNeg 1 ⊢ n ≤ n + 1
n : ℤ this : NonNeg 1 ⊢ NonNeg 1
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.le_succ
[105, 1]
[107, 14]
trivial
n : ℤ this : NonNeg 1 ⊢ NonNeg 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.succ_le_succ
[109, 1]
[110, 8]
sorry
n m : ℤ ⊢ n ≤ m → n + 1 ≤ m + 1
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.ge_trans
[112, 1]
[115, 23]
simp [GE.ge]
n k m : ℤ ⊢ n ≥ m → m ≥ k → n ≥ k
n k m : ℤ ⊢ m ≤ n → k ≤ m → k ≤ n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.ge_trans
[112, 1]
[115, 23]
intros h₁ h₂
n k m : ℤ ⊢ m ≤ n → k ≤ m → k ≤ n
n k m : ℤ h₁ : m ≤ n h₂ : k ≤ m ⊢ k ≤ n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.ge_trans
[112, 1]
[115, 23]
apply le_trans h₂ h₁
n k m : ℤ h₁ : m ≤ n h₂ : k ≤ m ⊢ k ≤ n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.lt_add_right
[117, 1]
[118, 8]
sorry
n m : ℤ ⊢ m > 0 → n < n + m
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mul_ge_zero
[120, 1]
[123, 34]
rw [Int.ge_zero_eq_nonneg, Int.ge_zero_eq_nonneg, Int.ge_zero_eq_nonneg]
n m : ℤ ⊢ n ≥ 0 → m ≥ 0 → n * m ≥ 0
n m : ℤ ⊢ NonNeg n → NonNeg m → NonNeg (n * m)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mul_ge_zero
[120, 1]
[123, 34]
intros hn hm
n m : ℤ ⊢ NonNeg n → NonNeg m → NonNeg (n * m)
n m : ℤ hn : NonNeg n hm : NonNeg m ⊢ NonNeg (n * m)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mul_ge_zero
[120, 1]
[123, 34]
cases hn
n m : ℤ hn : NonNeg n hm : NonNeg m ⊢ NonNeg (n * m)
case mk m : ℤ hm : NonNeg m n✝ : ℕ ⊢ NonNeg (ofNat n✝ * m)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mul_ge_zero
[120, 1]
[123, 34]
cases hm
case mk m : ℤ hm : NonNeg m n✝ : ℕ ⊢ NonNeg (ofNat n✝ * m)
case mk.mk n✝¹ n✝ : ℕ ⊢ NonNeg (ofNat n✝¹ * ofNat n✝)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mul_ge_zero
[120, 1]
[123, 34]
constructor
case mk.mk n✝¹ n✝ : ℕ ⊢ NonNeg (ofNat n✝¹ * ofNat n✝)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.mul_gt_zero
[125, 1]
[126, 8]
sorry
n m : ℤ ⊢ n > 0 → m > 0 → n * m > 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_ge_zero
[128, 1]
[131, 50]
revert n
n : ℤ m : ℕ ⊢ n ≥ 0 → n ^ m ≥ 0
m : ℕ ⊢ ∀ (n : ℤ), n ≥ 0 → n ^ m ≥ 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_ge_zero
[128, 1]
[131, 50]
induction m <;> intros n h <;> simp
m : ℕ ⊢ ∀ (n : ℤ), n ≥ 0 → n ^ m ≥ 0
case succ n✝ : ℕ n_ih✝ : ∀ (n : ℤ), n ≥ 0 → n ^ n✝ ≥ 0 n : ℤ h : n ≥ 0 ⊢ 0 ≤ n ^ Nat.succ n✝
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_ge_zero
[128, 1]
[131, 50]
case succ acc ih => simp [pow_succ]; apply mul_ge_zero (ih _ h) h
acc : ℕ ih : ∀ (n : ℤ), n ≥ 0 → n ^ acc ≥ 0 n : ℤ h : n ≥ 0 ⊢ 0 ≤ n ^ Nat.succ acc
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_ge_zero
[128, 1]
[131, 50]
simp [pow_succ]
acc : ℕ ih : ∀ (n : ℤ), n ≥ 0 → n ^ acc ≥ 0 n : ℤ h : n ≥ 0 ⊢ 0 ≤ n ^ Nat.succ acc
acc : ℕ ih : ∀ (n : ℤ), n ≥ 0 → n ^ acc ≥ 0 n : ℤ h : n ≥ 0 ⊢ 0 ≤ n ^ acc * n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_ge_zero
[128, 1]
[131, 50]
apply mul_ge_zero (ih _ h) h
acc : ℕ ih : ∀ (n : ℤ), n ≥ 0 → n ^ acc ≥ 0 n : ℤ h : n ≥ 0 ⊢ 0 ≤ n ^ acc * n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_gt_zero
[133, 1]
[136, 50]
revert n
n : ℤ m : ℕ ⊢ n > 0 → n ^ m > 0
m : ℕ ⊢ ∀ (n : ℤ), n > 0 → n ^ m > 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_gt_zero
[133, 1]
[136, 50]
induction m <;> intros n h <;> simp
m : ℕ ⊢ ∀ (n : ℤ), n > 0 → n ^ m > 0
case succ n✝ : ℕ n_ih✝ : ∀ (n : ℤ), n > 0 → n ^ n✝ > 0 n : ℤ h : n > 0 ⊢ 0 < n ^ Nat.succ n✝
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_gt_zero
[133, 1]
[136, 50]
case succ acc ih => simp [pow_succ]; apply mul_gt_zero (ih _ h) h
acc : ℕ ih : ∀ (n : ℤ), n > 0 → n ^ acc > 0 n : ℤ h : n > 0 ⊢ 0 < n ^ Nat.succ acc
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_gt_zero
[133, 1]
[136, 50]
simp [pow_succ]
acc : ℕ ih : ∀ (n : ℤ), n > 0 → n ^ acc > 0 n : ℤ h : n > 0 ⊢ 0 < n ^ Nat.succ acc
acc : ℕ ih : ∀ (n : ℤ), n > 0 → n ^ acc > 0 n : ℤ h : n > 0 ⊢ 0 < n ^ acc * n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.pow_gt_zero
[133, 1]
[136, 50]
apply mul_gt_zero (ih _ h) h
acc : ℕ ih : ∀ (n : ℤ), n > 0 → n ^ acc > 0 n : ℤ h : n > 0 ⊢ 0 < n ^ acc * n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.lt_add_lt_left
[138, 1]
[139, 8]
sorry
n m k : ℤ ⊢ n < m → k + n < k + m
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Int.ge_add_ge_right
[141, 1]
[142, 8]
sorry
n m k : ℤ ⊢ n ≥ m → n + k ≥ m + k
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Nat.minus_plus_one
[150, 1]
[151, 26]
cases a
a : ℕ h : a > 0 ⊢ a - 1 + 1 = a
case zero h : zero > 0 ⊢ zero - 1 + 1 = zero case succ n✝ : ℕ h : succ n✝ > 0 ⊢ succ n✝ - 1 + 1 = succ n✝
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Nat.minus_plus_one
[150, 1]
[151, 26]
simp at h
case zero h : zero > 0 ⊢ zero - 1 + 1 = zero case succ n✝ : ℕ h : succ n✝ > 0 ⊢ succ n✝ - 1 + 1 = succ n✝
case succ n✝ : ℕ h : succ n✝ > 0 ⊢ succ n✝ - 1 + 1 = succ n✝
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/Arith.lean
Nat.minus_plus_one
[150, 1]
[151, 26]
rfl
case succ n✝ : ℕ h : succ n✝ > 0 ⊢ succ n✝ - 1 + 1 = succ n✝
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_remap_bound
[22, 1]
[26, 8]
intro i h
n m : ℕ ⊢ ∀ (i : ℕ), i < n * m → transpose_remap n m i < n * m
n m i : ℕ h : i < n * m ⊢ transpose_remap n m i < n * m
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_remap_bound
[22, 1]
[26, 8]
simp [transpose_remap]
n m i : ℕ h : i < n * m ⊢ transpose_remap n m i < n * m
n m i : ℕ h : i < n * m ⊢ m * (i % n) + i / n < n * m
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_remap_bound
[22, 1]
[26, 8]
sorry
n m i : ℕ h : i < n * m ⊢ m * (i % n) + i / n < n * m
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_remap_involutive
[28, 1]
[31, 8]
simp [transpose_remap, Function.comp]
n m : ℕ ⊢ ∀ (i : ℕ), transpose_remap m n (transpose_remap n m i) = i
n m : ℕ ⊢ ∀ (i : ℕ), n * ((m * (i % n) + i / n) % m) + (m * (i % n) + i / n) / m = i
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_remap_involutive
[28, 1]
[31, 8]
intro i
n m : ℕ ⊢ ∀ (i : ℕ), n * ((m * (i % n) + i / n) % m) + (m * (i % n) + i / n) / m = i
n m i : ℕ ⊢ n * ((m * (i % n) + i / n) % m) + (m * (i % n) + i / n) / m = i
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_remap_involutive
[28, 1]
[31, 8]
sorry
n m i : ℕ ⊢ n * ((m * (i % n) + i / n) % m) + (m * (i % n) + i / n) / m = i
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
Function.comp_assoc
[50, 1]
[52, 20]
funext x
α : Sort u_1 β : Sort u_2 γ : Sort u_3 δ : Sort u_4 f : α → β g : β → γ h : γ → δ ⊢ (h ∘ g) ∘ f = h ∘ g ∘ f
case h α : Sort u_1 β : Sort u_2 γ : Sort u_3 δ : Sort u_4 f : α → β g : β → γ h : γ → δ x : α ⊢ comp (h ∘ g) f x = comp h (g ∘ f) x
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
Function.comp_assoc
[50, 1]
[52, 20]
simp
case h α : Sort u_1 β : Sort u_2 γ : Sort u_3 δ : Sort u_4 f : α → β g : β → γ h : γ → δ x : α ⊢ comp (h ∘ g) f x = comp h (g ∘ f) x
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_involutive
[54, 1]
[62, 38]
intro t
α n : ℕ m : MLIR.AST.MLIRTy ⊢ ∀ (t : Matrix α n m), transpose (transpose t) = t
α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ transpose (transpose t) = t
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_involutive
[54, 1]
[62, 38]
simp [transpose]
α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ transpose (transpose t) = t
α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ { toTensor := { shape := [α, n], data := List.remap (List.remap t.toTensor.data (transpose_remap α n) (_ : ∀ (i : ℕ), i < List.length t.toTensor.data → transpose_remap α n i < List.length t.toTensor.data)) ...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_involutive
[54, 1]
[62, 38]
apply RankedTensor.eq_of_fields_eq <;> simp
α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ { toTensor := { shape := [α, n], data := List.remap (List.remap t.toTensor.data (transpose_remap α n) (_ : ∀ (i : ℕ), i < List.length t.toTensor.data → transpose_remap α n i < List.length t.toTensor.data)) ...
case a α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ [α, n] = t.toTensor.shape case a α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ List.remap (List.remap t.toTensor.data (transpose_remap α n) (_ : ∀ (i : ℕ), i < List.length t.toTensor.data → transpose_remap α n i < List.length t.toTensor.data)) ...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_involutive
[54, 1]
[62, 38]
. rw [←dim_known_project_eq _ t.h_refines] <;> simp
case a α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ [α, n] = t.toTensor.shape case a α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ List.remap (List.remap t.toTensor.data (transpose_remap α n) (_ : ∀ (i : ℕ), i < List.length t.toTensor.data → transpose_remap α n i < List.length t.toTensor.data)) ...
case a α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ List.remap (List.remap t.toTensor.data (transpose_remap α n) (_ : ∀ (i : ℕ), i < List.length t.toTensor.data → transpose_remap α n i < List.length t.toTensor.data)) (transpose_remap n α) (_ : ∀ (n_1 : ℕ), n_1 < ...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ToyModel.lean
transpose_involutive
[54, 1]
[62, 38]
. simp [List.remap_remap] apply List.extF <;> simp simp [transpose_remap_involutive]
case a α n : ℕ m : MLIR.AST.MLIRTy t : Matrix α n m ⊢ List.remap (List.remap t.toTensor.data (transpose_remap α n) (_ : ∀ (i : ℕ), i < List.length t.toTensor.data → transpose_remap α n i < List.length t.toTensor.data)) (transpose_remap n α) (_ : ∀ (n_1 : ℕ), n_1 < ...
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.id_map
[8, 1]
[13, 34]
simp [Functor.map]
E : Type → Type R : Type t : Fitree E R ⊢ id <$> t = t
E : Type → Type R : Type t : Fitree E R ⊢ bind t (ret ∘ id) = t
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.id_map
[8, 1]
[13, 34]
induction t with | Ret _ => rfl | Vis _ _ ih => simp [bind, ih]
E : Type → Type R : Type t : Fitree E R ⊢ bind t (ret ∘ id) = t
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.id_map
[8, 1]
[13, 34]
rfl
case Ret E : Type → Type R : Type r✝ : R ⊢ bind (Ret r✝) (ret ∘ id) = Ret r✝
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.id_map
[8, 1]
[13, 34]
simp [bind, ih]
case Vis E : Type → Type R T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R ih : ∀ (a : T✝), bind (k✝ a) (ret ∘ id) = k✝ a ⊢ bind (Vis e✝ k✝) (ret ∘ id) = Vis e✝ k✝
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.comp_map
[15, 1]
[20, 34]
simp [Functor.map]
R₁ R₂ R₃ : Type E : Type → Type f : R₁ → R₂ g : R₂ → R₃ t : Fitree E R₁ ⊢ (g ∘ f) <$> t = g <$> f <$> t
R₁ R₂ R₃ : Type E : Type → Type f : R₁ → R₂ g : R₂ → R₃ t : Fitree E R₁ ⊢ bind t (ret ∘ g ∘ f) = bind t fun x => ret (g (f x))
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.comp_map
[15, 1]
[20, 34]
induction t with | Ret _ => rfl | Vis _ _ ih => simp [bind, ih]
R₁ R₂ R₃ : Type E : Type → Type f : R₁ → R₂ g : R₂ → R₃ t : Fitree E R₁ ⊢ bind t (ret ∘ g ∘ f) = bind t fun x => ret (g (f x))
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.comp_map
[15, 1]
[20, 34]
rfl
case Ret R₁ R₂ R₃ : Type E : Type → Type f : R₁ → R₂ g : R₂ → R₃ r✝ : R₁ ⊢ bind (Ret r✝) (ret ∘ g ∘ f) = bind (Ret r✝) fun x => ret (g (f x))
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.comp_map
[15, 1]
[20, 34]
simp [bind, ih]
case Vis R₁ R₂ R₃ : Type E : Type → Type f : R₁ → R₂ g : R₂ → R₃ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), bind (k✝ a) (ret ∘ g ∘ f) = bind (k✝ a) fun x => ret (g (f x)) ⊢ bind (Vis e✝ k✝) (ret ∘ g ∘ f) = bind (Vis e✝ k✝) fun x => ret (g (f x))
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqLeft_eq
[27, 1]
[32, 58]
simp [SeqLeft.seqLeft, Seq.seq]
E : Type → Type R₁ R₂ : Type t₁ : Fitree E R₁ t₂ : Fitree E R₂ ⊢ (SeqLeft.seqLeft t₁ fun x => t₂) = Seq.seq (Function.const R₂ <$> t₁) fun x => t₂
E : Type → Type R₁ R₂ : Type t₁ : Fitree E R₁ t₂ : Fitree E R₂ ⊢ (bind t₁ fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> t₁) fun y => bind t₂ (ret ∘ y)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqLeft_eq
[27, 1]
[32, 58]
induction t₁ with | Ret _ => rfl | Vis _ _ ih => simp [bind]; funext _; simp [ih]; sorry
E : Type → Type R₁ R₂ : Type t₁ : Fitree E R₁ t₂ : Fitree E R₂ ⊢ (bind t₁ fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> t₁) fun y => bind t₂ (ret ∘ y)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqLeft_eq
[27, 1]
[32, 58]
rfl
case Ret E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ r✝ : R₁ ⊢ (bind (Ret r✝) fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> Ret r✝) fun y => bind t₂ (ret ∘ y)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqLeft_eq
[27, 1]
[32, 58]
simp [bind]
case Vis E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> k✝ a) fun y => bind t₂ (ret ∘ y) ⊢ (bind (Vis e✝ k✝) fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> Vis e✝ k...
case Vis E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> k✝ a) fun y => bind t₂ (ret ∘ y) ⊢ (fun r => bind (k✝ r) fun a => bind t₂ fun x => ret a) = fun r => bind (k✝ r) fun x =...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqLeft_eq
[27, 1]
[32, 58]
funext _
case Vis E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> k✝ a) fun y => bind t₂ (ret ∘ y) ⊢ (fun r => bind (k✝ r) fun a => bind t₂ fun x => ret a) = fun r => bind (k✝ r) fun x =...
case Vis.h E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> k✝ a) fun y => bind t₂ (ret ∘ y) x✝ : T✝ ⊢ (bind (k✝ x✝) fun a => bind t₂ fun x => ret a) = bind (k✝ x✝) fun x => bind t₂ ...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqLeft_eq
[27, 1]
[32, 58]
simp [ih]
case Vis.h E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> k✝ a) fun y => bind t₂ (ret ∘ y) x✝ : T✝ ⊢ (bind (k✝ x✝) fun a => bind t₂ fun x => ret a) = bind (k✝ x✝) fun x => bind t₂ ...
case Vis.h E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> k✝ a) fun y => bind t₂ (ret ∘ y) x✝ : T✝ ⊢ (bind (Function.const R₂ <$> k✝ x✝) fun y => bind t₂ (ret ∘ y)) = bind (k✝ ...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqLeft_eq
[27, 1]
[32, 58]
sorry
case Vis.h E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun a => bind t₂ fun x => ret a) = bind (Function.const R₂ <$> k✝ a) fun y => bind t₂ (ret ∘ y) x✝ : T✝ ⊢ (bind (Function.const R₂ <$> k✝ x✝) fun y => bind t₂ (ret ∘ y)) = bind (k✝ ...
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqRight_eq
[34, 1]
[41, 44]
simp [SeqRight.seqRight, Seq.seq]
E : Type → Type R₁ R₂ : Type t₁ : Fitree E R₁ t₂ : Fitree E R₂ ⊢ (SeqRight.seqRight t₁ fun x => t₂) = Seq.seq (Function.const R₁ id <$> t₁) fun x => t₂
E : Type → Type R₁ R₂ : Type t₁ : Fitree E R₁ t₂ : Fitree E R₂ ⊢ (bind t₁ fun x => t₂) = bind (Function.const R₁ id <$> t₁) fun y => bind t₂ (ret ∘ y)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqRight_eq
[34, 1]
[41, 44]
induction t₁ with | Ret _ => simp [Function.const, Function.comp, bind] | Vis _ _ ih => simp [bind]; funext _; simp [ih]; sorry
E : Type → Type R₁ R₂ : Type t₁ : Fitree E R₁ t₂ : Fitree E R₂ ⊢ (bind t₁ fun x => t₂) = bind (Function.const R₁ id <$> t₁) fun y => bind t₂ (ret ∘ y)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqRight_eq
[34, 1]
[41, 44]
simp [Function.const, Function.comp, bind]
case Ret E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ r✝ : R₁ ⊢ (bind (Ret r✝) fun x => t₂) = bind (Function.const R₁ id <$> Ret r✝) fun y => bind t₂ (ret ∘ y)
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqRight_eq
[34, 1]
[41, 44]
simp [bind]
case Vis E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun x => t₂) = bind (Function.const R₁ id <$> k✝ a) fun y => bind t₂ (ret ∘ y) ⊢ (bind (Vis e✝ k✝) fun x => t₂) = bind (Function.const R₁ id <$> Vis e✝ k✝) fun y => bind t₂ (ret ∘ y)
case Vis E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun x => t₂) = bind (Function.const R₁ id <$> k✝ a) fun y => bind t₂ (ret ∘ y) ⊢ (fun r => bind (k✝ r) fun x => t₂) = fun r => bind (k✝ r) fun x => bind t₂ (ret ∘ id)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqRight_eq
[34, 1]
[41, 44]
funext _
case Vis E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun x => t₂) = bind (Function.const R₁ id <$> k✝ a) fun y => bind t₂ (ret ∘ y) ⊢ (fun r => bind (k✝ r) fun x => t₂) = fun r => bind (k✝ r) fun x => bind t₂ (ret ∘ id)
case Vis.h E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun x => t₂) = bind (Function.const R₁ id <$> k✝ a) fun y => bind t₂ (ret ∘ y) x✝ : T✝ ⊢ (bind (k✝ x✝) fun x => t₂) = bind (k✝ x✝) fun x => bind t₂ (ret ∘ id)
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqRight_eq
[34, 1]
[41, 44]
simp [ih]
case Vis.h E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun x => t₂) = bind (Function.const R₁ id <$> k✝ a) fun y => bind t₂ (ret ∘ y) x✝ : T✝ ⊢ (bind (k✝ x✝) fun x => t₂) = bind (k✝ x✝) fun x => bind t₂ (ret ∘ id)
case Vis.h E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun x => t₂) = bind (Function.const R₁ id <$> k✝ a) fun y => bind t₂ (ret ∘ y) x✝ : T✝ ⊢ (bind (Function.const R₁ id <$> k✝ x✝) fun y => bind t₂ (ret ∘ y)) = bind (k✝ x✝) fun x => bind t₂ (re...
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seqRight_eq
[34, 1]
[41, 44]
sorry
case Vis.h E : Type → Type R₁ R₂ : Type t₂ : Fitree E R₂ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), (bind (k✝ a) fun x => t₂) = bind (Function.const R₁ id <$> k✝ a) fun y => bind t₂ (ret ∘ y) x✝ : T✝ ⊢ (bind (Function.const R₁ id <$> k✝ x✝) fun y => bind t₂ (ret ∘ y)) = bind (k✝ x✝) fun x => bind t₂ (re...
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.seq_assoc
[55, 1]
[58, 8]
sorry
E : Type → Type R₁ R₂ R₃ : Type t₁ : Fitree E R₁ t₂ : Fitree E (R₁ → R₂) t₃ : Fitree E (R₂ → R₃) ⊢ (Seq.seq t₃ fun x => Seq.seq t₂ fun x => t₁) = Seq.seq (Seq.seq (Function.comp <$> t₃) fun x => t₂) fun x => t₁
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.bind_assoc
[81, 1]
[86, 31]
induction t with | Ret _ => rfl | Vis _ _ ih => simp [bind];
E : Type → Type R₁ R₂ R₃ : Type t : Fitree E R₁ k₁ : R₁ → Fitree E R₂ k₂ : R₂ → Fitree E R₃ ⊢ bind (bind t k₁) k₂ = bind t fun x => bind (k₁ x) k₂
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.bind_assoc
[81, 1]
[86, 31]
rfl
case Ret E : Type → Type R₁ R₂ R₃ : Type k₁ : R₁ → Fitree E R₂ k₂ : R₂ → Fitree E R₃ r✝ : R₁ ⊢ bind (bind (Ret r✝) k₁) k₂ = bind (Ret r✝) fun x => bind (k₁ x) k₂
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Semantics/FitreeLaws.lean
Fitree.bind_assoc
[81, 1]
[86, 31]
simp [bind]
case Vis E : Type → Type R₁ R₂ R₃ : Type k₁ : R₁ → Fitree E R₂ k₂ : R₂ → Fitree E R₃ T✝ : Type e✝ : E T✝ k✝ : T✝ → Fitree E R₁ ih : ∀ (a : T✝), bind (bind (k✝ a) k₁) k₂ = bind (k✝ a) fun x => bind (k₁ x) k₂ ⊢ bind (bind (Vis e✝ k✝) k₁) k₂ = bind (Vis e✝ k✝) fun x => bind (k₁ x) k₂
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
reading/tactic.lean
tst3
[21, 1]
[25, 2]
intros h1 h2
p q : Prop ⊢ p → q → p
p q : Prop h1 : p h2 : q ⊢ p
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
reading/tactic.lean
tst3
[21, 1]
[25, 2]
assumption
p q : Prop h1 : p h2 : q ⊢ p
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_ge
[40, 1]
[46, 8]
simp [mod2]
a : ℤ n : ℕ ⊢ mod2 a n ≥ 0
a : ℤ n : ℕ ⊢ 0 ≤ a % 2 ^ n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_ge
[40, 1]
[46, 8]
apply Int.mod_ge
a : ℤ n : ℕ ⊢ 0 ≤ a % 2 ^ n
case a a : ℤ n : ℕ ⊢ a ≥ 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_ge
[40, 1]
[46, 8]
have h := Int.ge_add_ge_right (2^n) (@Int.mod_ge_neg a (2^n))
case a a : ℤ n : ℕ ⊢ a ≥ 0
case a a : ℤ n : ℕ h : a % 2 ^ n + 2 ^ n ≥ -2 ^ n + 2 ^ n ⊢ a ≥ 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_ge
[40, 1]
[46, 8]
rw [Int.add_left_neg] at h
case a a : ℤ n : ℕ h : a % 2 ^ n + 2 ^ n ≥ -2 ^ n + 2 ^ n ⊢ a ≥ 0
case a a : ℤ n : ℕ h : a % 2 ^ n + 2 ^ n ≥ 0 ⊢ a ≥ 0
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_ge
[40, 1]
[46, 8]
sorry
case a a : ℤ n : ℕ h : a % 2 ^ n + 2 ^ n ≥ 0 ⊢ a ≥ 0
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_lt
[49, 1]
[51, 35]
simp [mod2]
a : ℤ n : ℕ ⊢ mod2 a n < 2 ^ n
a : ℤ n : ℕ ⊢ a % 2 ^ n < 2 ^ n
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_lt
[49, 1]
[51, 35]
apply Int.mod_lt Int.two_pow_pos
a : ℤ n : ℕ ⊢ a % 2 ^ n < 2 ^ n
no goals
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_idem
[56, 1]
[60, 34]
intros h
n : ℕ a : ℤ ⊢ a ≥ 0 ∧ a < 2 ^ n → mod2 a n = a
n : ℕ a : ℤ h : a ≥ 0 ∧ a < 2 ^ n ⊢ mod2 a n = a
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_idem
[56, 1]
[60, 34]
simp [mod2]
n : ℕ a : ℤ h : a ≥ 0 ∧ a < 2 ^ n ⊢ mod2 a n = a
n : ℕ a : ℤ h : a ≥ 0 ∧ a < 2 ^ n ⊢ a % 2 ^ n = a
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/FinInt.lean
FinInt.mod2_idem
[56, 1]
[60, 34]
simp [Int.mod_bounds _ h.1 h.2]
n : ℕ a : ℤ h : a ≥ 0 ∧ a < 2 ^ n ⊢ a % 2 ^ n = a
no goals