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 | input stringlengths 73 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 | Please generate a tactic in lean4 to solve the state.
STATE:
x y : ℤ
n : ℕ
⊢ x = y → mod2 x n = mod2 y n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
x y : ℤ
n : ℕ
h : x = y
⊢ mod2 x n = mod2 y n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
⊢ mod2 0 n = 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
⊢ 2 ^ n % 2 ^ n = 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
⊢ mod2 (2 ^ n) n = 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
⊢ 2 ^ n % 2 ^ n = 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
x : ℤ
⊢ mod2 (2 ^ n + x) n = mod2 x n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
x : ℤ
n : ℕ
⊢ mod2 (x + 2 ^ n) n = mod2 x n
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℤ
n : ℕ
⊢ smod2 a n ≥ -2 ^ n
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
a : ℤ
n : ℕ
h✝ : ¬2 ^ n ≤ mod2 a (n + 1)
⊢ -2 ^ n ≤ mod2 a (n + 1)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℤ
n : ℕ
⊢ smod2 a n < 2 ^ n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case inr
a : ℤ
n : ℕ
h✝ : ¬2 ^ n ≤ mod2 a (n + 1)
⊢ mod2 a (n + 1) < 2 ^ n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
a : ℤ
⊢ a ≥ -2 ^ n ∧ a < 2 ^ n → smod2 a n = a
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℤ
n : ℕ
⊢ smod2 a n = mod2 (a + 2 ^ n) (n + 1) - 2 ^ n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a b : ℤ
n : ℕ
⊢ a ≡ b [2^n] → a ≥ 0 ∧ a < 2 ^ n → b ≥ 0 ∧ b < 2 ^ n → a = b
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a b : ℤ
n : ℕ
h : a ≡ b [2^n]
ha : a ≥ 0 ∧ a < 2 ^ n
hb : b ≥ 0 ∧ b < 2 ^ n
⊢ a = b
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a b : ℤ
n : ℕ
⊢ a ≡ b [±2^n] → a ≥ -2 ^ n ∧ a < 2 ^ n → b ≥ -2 ^ n ∧ b < 2 ^ n → a = b
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℤ
n : ℕ
b : ℤ
⊢ mod2 (mod2 a n + b) n = mod2 (a + b) n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a b : ℤ
n : ℕ
⊢ mod2 (a + mod2 b n) n = mod2 (a + b) n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℤ
n : ℕ
⊢ mod2 (-mod2 a n) n = mod2 (-a) n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a b : ℤ
n : ℕ
⊢ mod2 (a - mod2 b n) n = mod2 (a - b) n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a : ℤ
n : ℕ
b : ℤ
⊢ mod2 (mod2 a n - b) n = mod2 (a - b) n
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
a b : ℤ
⊢ a ≡ b [2^n] → a ≡ mod2 b n [2^n]
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℕ
a b : ℤ
⊢ a ≡ b [2^n] → mod2 a n ≡ b [2^n]
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : FinInt sz
⊢ toUint n ≥ 0
TACTIC:
|
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✝) | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
⊢ ∀ {n : FinInt sz}, toUint n ≥ 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
bn : Bool
n' : FinInt sz
ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0
⊢ 0 ≤ toUint (next bn n')
TACTIC:
|
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' | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
bn : Bool
n' : FinInt sz
ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0
⊢ 0 ≤ toUint (next bn n')
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case true
sz : ℕ
n' : FinInt sz
ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0
⊢ 0 ≤ 2 ^ sz + toUint n'
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case true.a
sz : ℕ
n' : FinInt sz
ih : ∀ {n : FinInt (Nat.add sz 0)}, toUint n ≥ 0
⊢ toUint n' ≥ 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : FinInt sz
⊢ toUint n < 2 ^ sz
TACTIC:
|
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✝ | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
⊢ ∀ {n : FinInt sz}, toUint n < 2 ^ sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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✝
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : FinInt (sz + 1)
⊢ toSint n ≥ -2 ^ sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : FinInt (sz + 1)
⊢ toSint n < 2 ^ sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
bn : Bool
n' : FinInt sz
⊢ toSint (next bn n') < 2 ^ sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
bn : Bool
n' : FinInt sz
⊢ toSint (next bn n') < 2 ^ sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case false
sz : ℕ
n' : FinInt sz
⊢ toUint n' < 2 ^ sz
case true
sz : ℕ
n' : FinInt sz
⊢ toUint n' - 2 ^ sz < 2 ^ sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case true
sz : ℕ
n' : FinInt sz
⊢ toUint n' - 2 ^ sz < 2 ^ sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
⊢ toUint zero = 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
⊢ toUint zero = 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
n : ℕ
ih : toUint zero = 0
⊢ toUint zero = 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
⊢ sz > 0 → toUint one = 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
h : sz > 0
⊢ toUint one = 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
h : Nat.zero > 0
⊢ toUint one = 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
h : Nat.zero > 0
⊢ ¬0 > 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
n : ℕ
ih : n > 0 → toUint one = 1
h : Nat.succ n > 0
⊢ toUint one = 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ.succ
n✝ : ℕ
ih : Nat.succ n✝ > 0 → toUint one = 1
h : Nat.succ (Nat.succ n✝) > 0
⊢ toUint one = 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ.succ
n✝ : ℕ
ih : Nat.succ n✝ > 0 → toUint one = 1
h : Nat.succ (Nat.succ n✝) > 0
⊢ Nat.succ n✝ > 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
⊢ toUint minusOne = 2 ^ sz - 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case zero
⊢ toUint minusOne = 2 ^ Nat.zero - 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
n : ℕ
ih : toUint minusOne = 2 ^ n - 1
⊢ toUint minusOne = 2 ^ Nat.succ n - 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ
n : ℕ
ih : toUint minusOne = 2 ^ n - 1
⊢ 2 ^ n + (2 ^ n - 1) = 2 ^ Nat.succ n - 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
b : Bool
n : FinInt sz
⊢ toUint (next b n) < 2 ^ sz ↔ b = false
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : FinInt (sz + 1)
⊢ toSint n =
match n with
| next false a => toUint n
| next true a => toUint n - 2 ^ (sz + 1)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : FinInt (sz + 1)
m : FinInt sz
⊢ toUint m - 2 ^ sz = 2 ^ sz + toUint m - 2 ^ (sz + 1)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : FinInt (sz + 1)
⊢ toUint n =
match n with
| next false a => toSint n
| next true a => toSint n + 2 ^ (sz + 1)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : FinInt (sz + 1)
m : FinInt sz
⊢ 2 ^ sz + toUint m = toUint m - 2 ^ sz + 2 ^ (sz + 1)
TACTIC:
|
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✝) | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : ℤ
⊢ toUint (ofInt sz n) = mod2 n sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℤ
⊢ toUint (ofInt Nat.zero n) = mod2 n Nat.zero
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℤ
sz : ℕ
ih : toUint (ofInt sz n) = mod2 n sz
⊢ toUint (ofInt (Nat.succ sz) n) = mod2 n (Nat.succ sz)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℤ
⊢ toUint (ofInt Nat.zero n) = mod2 n Nat.zero
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℤ
⊢ 0 = n % 1
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℤ
sz : ℕ
ih : toUint (ofInt sz n) = mod2 n sz
⊢ toUint (ofInt (Nat.succ sz) n) = mod2 n (Nat.succ sz)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz n : ℕ
⊢ toUint (OfNat.ofNat n) = mod2 (↑n) sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : ℤ
⊢ toSint (ofInt (sz + 1) n) = smod2 n sz
TACTIC:
|
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✝ | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
n : ℤ
⊢ toUint (FinInt.ofIntAux sz n).fst = mod2 n sz ∧ (FinInt.ofIntAux sz n).snd = n / 2 ^ sz
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℤ
⊢ toUint (FinInt.ofIntAux Nat.zero n).fst = mod2 n Nat.zero ∧ (FinInt.ofIntAux Nat.zero n).snd = n / 2 ^ Nat.zero
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℤ
⊢ toUint (FinInt.ofIntAux Nat.zero n).fst = mod2 n Nat.zero ∧ (FinInt.ofIntAux Nat.zero n).snd = n / 2 ^ Nat.zero
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
n : ℤ
⊢ 0 = mod2 n 0
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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) | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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)
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
sz : ℕ
a b : FinInt sz
⊢ toUint a = toUint b → a = b
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a b : FinInt Nat.zero
h : toUint a = toUint b
⊢ a = b
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
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
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
a b : FinInt Nat.zero
h : toUint a = toUint b
⊢ a = b
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case nil
b : FinInt Nat.zero
h : toUint nil = toUint b
⊢ nil = b
TACTIC:
|
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 | Please generate a tactic in lean4 to solve the state.
STATE:
case nil.nil
h : toUint nil = toUint nil
⊢ nil = nil
TACTIC:
|
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