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/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_left_cancel | [118, 11] | [132, 36] | rfl | case one_one
x : Pos
h : x * 1 = x * 1
⊢ 1 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case one_one
x : Pos
h : x * 1 = x * 1
⊢ 1 = 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_left_cancel | [118, 11] | [132, 36] | rw [Pos.mul_one, Pos.mul_succ] at h | case one_succ
x z : Pos
a✝ : x * 1 = x * z → 1 = z
h : x * 1 = x * (z + 1)
⊢ 1 = z + 1 | case one_succ
x z : Pos
a✝ : x * 1 = x * z → 1 = z
h : x = x * z + x
⊢ 1 = z + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case one_succ
x z : Pos
a✝ : x * 1 = x * z → 1 = z
h : x * 1 = x * (z + 1)
⊢ 1 = z + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_left_cancel | [118, 11] | [132, 36] | absurd h | case one_succ
x z : Pos
a✝ : x * 1 = x * z → 1 = z
h : x = x * z + x
⊢ 1 = z + 1 | case one_succ
x z : Pos
a✝ : x * 1 = x * z → 1 = z
h : x = x * z + x
⊢ ¬x = x * z + x | Please generate a tactic in lean4 to solve the state.
STATE:
case one_succ
x z : Pos
a✝ : x * 1 = x * z → 1 = z
h : x = x * z + x
⊢ 1 = z + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_left_cancel | [118, 11] | [132, 36] | apply Pos.ne_add_self_left | case one_succ
x z : Pos
a✝ : x * 1 = x * z → 1 = z
h : x = x * z + x
⊢ ¬x = x * z + x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case one_succ
x z : Pos
a✝ : x * 1 = x * z → 1 = z
h : x = x * z + x
⊢ ¬x = x * z + x
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_left_cancel | [118, 11] | [132, 36] | rw [Pos.mul_one, Pos.mul_succ] at h | case succ_one
x y : Pos
a✝ : x * y = x * 1 → y = 1
h : x * (y + 1) = x * 1
⊢ y + 1 = 1 | case succ_one
x y : Pos
a✝ : x * y = x * 1 → y = 1
h : x * y + x = x
⊢ y + 1 = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_one
x y : Pos
a✝ : x * y = x * 1 → y = 1
h : x * (y + 1) = x * 1
⊢ y + 1 = 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_left_cancel | [118, 11] | [132, 36] | absurd h.symm | case succ_one
x y : Pos
a✝ : x * y = x * 1 → y = 1
h : x * y + x = x
⊢ y + 1 = 1 | case succ_one
x y : Pos
a✝ : x * y = x * 1 → y = 1
h : x * y + x = x
⊢ ¬x = x * y + x | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_one
x y : Pos
a✝ : x * y = x * 1 → y = 1
h : x * y + x = x
⊢ y + 1 = 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_left_cancel | [118, 11] | [132, 36] | apply Pos.ne_add_self_left | case succ_one
x y : Pos
a✝ : x * y = x * 1 → y = 1
h : x * y + x = x
⊢ ¬x = x * y + x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_one
x y : Pos
a✝ : x * y = x * 1 → y = 1
h : x * y + x = x
⊢ ¬x = x * y + x
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_left_cancel | [118, 11] | [132, 36] | rw [Pos.mul_succ, Pos.mul_succ] at h | case succ_succ
x y z : Pos
H : x * y = x * z → y = z
h : x * (y + 1) = x * (z + 1)
⊢ y + 1 = z + 1 | case succ_succ
x y z : Pos
H : x * y = x * z → y = z
h : x * y + x = x * z + x
⊢ y + 1 = z + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_succ
x y z : Pos
H : x * y = x * z → y = z
h : x * (y + 1) = x * (z + 1)
⊢ y + 1 = z + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_left_cancel | [118, 11] | [132, 36] | rw [H (Pos.add_right_cancel h)] | case succ_succ
x y z : Pos
H : x * y = x * z → y = z
h : x * y + x = x * z + x
⊢ y + 1 = z + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_succ
x y z : Pos
H : x * y = x * z → y = z
h : x * y + x = x * z + x
⊢ y + 1 = z + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | intro h | x y z : Pos
⊢ x * y = z * y → x = z | x y z : Pos
h : x * y = z * y
⊢ x = z | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
⊢ x * y = z * y → x = z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | induction x, z with
| one_one => rfl
| one_succ x _ =>
rw [Pos.one_mul, Pos.succ_mul] at h
absurd h
apply Pos.ne_add_self_left
| succ_one z _ =>
rw [Pos.one_mul, Pos.succ_mul] at h
absurd h.symm
apply Pos.ne_add_self_left
| succ_succ x z H =>
rw [Pos.succ_mul, Pos.succ_mul] at h
rw [H (Pos.add_right_can... | x y z : Pos
h : x * y = z * y
⊢ x = z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
h : x * y = z * y
⊢ x = z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | rfl | case one_one
y : Pos
h : 1 * y = 1 * y
⊢ 1 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case one_one
y : Pos
h : 1 * y = 1 * y
⊢ 1 = 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | rw [Pos.one_mul, Pos.succ_mul] at h | case one_succ
y x : Pos
a✝ : 1 * y = x * y → 1 = x
h : 1 * y = (x + 1) * y
⊢ 1 = x + 1 | case one_succ
y x : Pos
a✝ : 1 * y = x * y → 1 = x
h : y = x * y + y
⊢ 1 = x + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case one_succ
y x : Pos
a✝ : 1 * y = x * y → 1 = x
h : 1 * y = (x + 1) * y
⊢ 1 = x + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | absurd h | case one_succ
y x : Pos
a✝ : 1 * y = x * y → 1 = x
h : y = x * y + y
⊢ 1 = x + 1 | case one_succ
y x : Pos
a✝ : 1 * y = x * y → 1 = x
h : y = x * y + y
⊢ ¬y = x * y + y | Please generate a tactic in lean4 to solve the state.
STATE:
case one_succ
y x : Pos
a✝ : 1 * y = x * y → 1 = x
h : y = x * y + y
⊢ 1 = x + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | apply Pos.ne_add_self_left | case one_succ
y x : Pos
a✝ : 1 * y = x * y → 1 = x
h : y = x * y + y
⊢ ¬y = x * y + y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case one_succ
y x : Pos
a✝ : 1 * y = x * y → 1 = x
h : y = x * y + y
⊢ ¬y = x * y + y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | rw [Pos.one_mul, Pos.succ_mul] at h | case succ_one
y z : Pos
a✝ : z * y = 1 * y → z = 1
h : (z + 1) * y = 1 * y
⊢ z + 1 = 1 | case succ_one
y z : Pos
a✝ : z * y = 1 * y → z = 1
h : z * y + y = y
⊢ z + 1 = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_one
y z : Pos
a✝ : z * y = 1 * y → z = 1
h : (z + 1) * y = 1 * y
⊢ z + 1 = 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | absurd h.symm | case succ_one
y z : Pos
a✝ : z * y = 1 * y → z = 1
h : z * y + y = y
⊢ z + 1 = 1 | case succ_one
y z : Pos
a✝ : z * y = 1 * y → z = 1
h : z * y + y = y
⊢ ¬y = z * y + y | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_one
y z : Pos
a✝ : z * y = 1 * y → z = 1
h : z * y + y = y
⊢ z + 1 = 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | apply Pos.ne_add_self_left | case succ_one
y z : Pos
a✝ : z * y = 1 * y → z = 1
h : z * y + y = y
⊢ ¬y = z * y + y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_one
y z : Pos
a✝ : z * y = 1 * y → z = 1
h : z * y + y = y
⊢ ¬y = z * y + y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | rw [Pos.succ_mul, Pos.succ_mul] at h | case succ_succ
y x z : Pos
H : x * y = z * y → x = z
h : (x + 1) * y = (z + 1) * y
⊢ x + 1 = z + 1 | case succ_succ
y x z : Pos
H : x * y = z * y → x = z
h : x * y + y = z * y + y
⊢ x + 1 = z + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_succ
y x z : Pos
H : x * y = z * y → x = z
h : (x + 1) * y = (z + 1) * y
⊢ x + 1 = z + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_right_cancel | [134, 11] | [148, 36] | rw [H (Pos.add_right_cancel h)] | case succ_succ
y x z : Pos
H : x * y = z * y → x = z
h : x * y + y = z * y + y
⊢ x + 1 = z + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case succ_succ
y x z : Pos
H : x * y = z * y → x = z
h : x * y + y = z * y + y
⊢ x + 1 = z + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_zero | [150, 11] | [151, 33] | by_toNat | x : Pos
⊢ x ^ 0 = 1 | x : Pos
⊢ x.toNat ^ 0 = 1 | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x ^ 0 = 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_zero | [150, 11] | [151, 33] | exact Nat.pow_zero _ | x : Pos
⊢ x.toNat ^ 0 = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x.toNat ^ 0 = 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_one | [153, 11] | [154, 33] | by_toNat | x : Pos
⊢ x ^ 1 = x | x : Pos
⊢ x.toNat ^ 1 = x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x ^ 1 = x
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_one | [153, 11] | [154, 33] | exact Nat.pow_one .. | x : Pos
⊢ x.toNat ^ 1 = x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x.toNat ^ 1 = x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.one_pow | [156, 11] | [157, 33] | exact Nat.one_pow .. | x : Nat
⊢ 1 ^ x = 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Nat
⊢ 1 ^ x = 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_succ | [159, 11] | [160, 34] | by_toNat | x : Pos
y : Nat
⊢ x ^ (y + 1) = x ^ y * x | x : Pos
y : Nat
⊢ x.toNat ^ (y + 1) = x.toNat ^ y * x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
y : Nat
⊢ x ^ (y + 1) = x ^ y * x
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_succ | [159, 11] | [160, 34] | exact Nat.pow_succ .. | x : Pos
y : Nat
⊢ x.toNat ^ (y + 1) = x.toNat ^ y * x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
y : Nat
⊢ x.toNat ^ (y + 1) = x.toNat ^ y * x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_add | [162, 11] | [163, 33] | by_toNat | x : Pos
y z : Nat
⊢ x ^ (y + z) = x ^ y * x ^ z | x : Pos
y z : Nat
⊢ x.toNat ^ (y + z) = x.toNat ^ y * x.toNat ^ z | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
y z : Nat
⊢ x ^ (y + z) = x ^ y * x ^ z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_add | [162, 11] | [163, 33] | exact Nat.pow_add .. | x : Pos
y z : Nat
⊢ x.toNat ^ (y + z) = x.toNat ^ y * x.toNat ^ z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
y z : Nat
⊢ x.toNat ^ (y + z) = x.toNat ^ y * x.toNat ^ z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_pow | [165, 11] | [166, 33] | by_toNat | x y : Pos
z : Nat
⊢ (x * y) ^ z = x ^ z * y ^ z | x y : Pos
z : Nat
⊢ (x.toNat * y.toNat) ^ z = x.toNat ^ z * y.toNat ^ z | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
z : Nat
⊢ (x * y) ^ z = x ^ z * y ^ z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.mul_pow | [165, 11] | [166, 33] | exact Nat.mul_pow .. | x y : Pos
z : Nat
⊢ (x.toNat * y.toNat) ^ z = x.toNat ^ z * y.toNat ^ z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
z : Nat
⊢ (x.toNat * y.toNat) ^ z = x.toNat ^ z * y.toNat ^ z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_mul | [168, 11] | [169, 33] | by_toNat | x : Pos
y z : Nat
⊢ x ^ (y * z) = (x ^ y) ^ z | x : Pos
y z : Nat
⊢ x.toNat ^ (y * z) = (x.toNat ^ y) ^ z | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
y z : Nat
⊢ x ^ (y * z) = (x ^ y) ^ z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_mul | [168, 11] | [169, 33] | exact Nat.pow_mul .. | x : Pos
y z : Nat
⊢ x.toNat ^ (y * z) = (x.toNat ^ y) ^ z | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
y z : Nat
⊢ x.toNat ^ (y * z) = (x.toNat ^ y) ^ z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_mul' | [171, 11] | [172, 34] | by_toNat | x : Pos
y z : Nat
⊢ x ^ (y * z) = (x ^ z) ^ y | x : Pos
y z : Nat
⊢ x.toNat ^ (y * z) = (x.toNat ^ z) ^ y | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
y z : Nat
⊢ x ^ (y * z) = (x ^ z) ^ y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_mul' | [171, 11] | [172, 34] | exact Nat.pow_mul' .. | x : Pos
y z : Nat
⊢ x.toNat ^ (y * z) = (x.toNat ^ z) ^ y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
y z : Nat
⊢ x.toNat ^ (y * z) = (x.toNat ^ z) ^ y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.pow_assoc | [174, 11] | [175, 19] | rw [Pos.pow_mul] | x : Pos
y z : Nat
⊢ (x ^ y) ^ z = x ^ (y * z) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
y z : Nat
⊢ (x ^ y) ^ z = x ^ (y * z)
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_refl | [177, 11] | [178, 33] | by_toNat | x : Pos
⊢ x ≤ x | x : Pos
⊢ x.toNat ≥ x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x ≤ x
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_refl | [177, 11] | [178, 33] | exact Nat.le_refl .. | x : Pos
⊢ x.toNat ≥ x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x.toNat ≥ x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_trans | [180, 11] | [181, 31] | by_toNat | x y z : Pos
⊢ x ≤ y → y ≤ z → x ≤ z | x y z : Pos
⊢ y.toNat ≥ x.toNat → z.toNat ≥ y.toNat → z.toNat ≥ x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
⊢ x ≤ y → y ≤ z → x ≤ z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_trans | [180, 11] | [181, 31] | exact Nat.le_trans | x y z : Pos
⊢ y.toNat ≥ x.toNat → z.toNat ≥ y.toNat → z.toNat ≥ x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
⊢ y.toNat ≥ x.toNat → z.toNat ≥ y.toNat → z.toNat ≥ x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_antisymm | [183, 11] | [184, 34] | by_toNat | x y : Pos
⊢ x ≤ y → y ≤ x → x = y | x y : Pos
⊢ y.toNat ≥ x.toNat → x.toNat ≥ y.toNat → x.toNat = y.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x ≤ y → y ≤ x → x = y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_antisymm | [183, 11] | [184, 34] | exact Nat.le_antisymm | x y : Pos
⊢ y.toNat ≥ x.toNat → x.toNat ≥ y.toNat → x.toNat = y.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ y.toNat ≥ x.toNat → x.toNat ≥ y.toNat → x.toNat = y.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_irrefl | [186, 11] | [187, 34] | by_toNat | x : Pos
⊢ ¬x < x | x : Pos
⊢ ¬x.toNat > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬x < x
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_irrefl | [186, 11] | [187, 34] | exact Nat.lt_irrefl _ | x : Pos
⊢ ¬x.toNat > x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬x.toNat > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_trans | [189, 11] | [190, 31] | by_toNat | x y z : Pos
⊢ x < y → y < z → x < z | x y z : Pos
⊢ y.toNat > x.toNat → z.toNat > y.toNat → z.toNat > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
⊢ x < y → y < z → x < z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_trans | [189, 11] | [190, 31] | exact Nat.lt_trans | x y z : Pos
⊢ y.toNat > x.toNat → z.toNat > y.toNat → z.toNat > x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
⊢ y.toNat > x.toNat → z.toNat > y.toNat → z.toNat > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_of_le_of_lt | [192, 11] | [193, 37] | by_toNat | x y z : Pos
⊢ x ≤ y → y < z → x < z | x y z : Pos
⊢ y.toNat ≥ x.toNat → z.toNat > y.toNat → z.toNat > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
⊢ x ≤ y → y < z → x < z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_of_le_of_lt | [192, 11] | [193, 37] | exact Nat.lt_of_le_of_lt | x y z : Pos
⊢ y.toNat ≥ x.toNat → z.toNat > y.toNat → z.toNat > x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
⊢ y.toNat ≥ x.toNat → z.toNat > y.toNat → z.toNat > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_of_lt_of_le | [195, 11] | [196, 37] | by_toNat | x y z : Pos
⊢ x < y → y ≤ z → x < z | x y z : Pos
⊢ y.toNat > x.toNat → z.toNat ≥ y.toNat → z.toNat > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
⊢ x < y → y ≤ z → x < z
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_of_lt_of_le | [195, 11] | [196, 37] | exact Nat.lt_of_lt_of_le | x y z : Pos
⊢ y.toNat > x.toNat → z.toNat ≥ y.toNat → z.toNat > x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y z : Pos
⊢ y.toNat > x.toNat → z.toNat ≥ y.toNat → z.toNat > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_of_eq | [198, 11] | [199, 31] | by_toNat | x y : Pos
⊢ x = y → x ≤ y | x y : Pos
⊢ x.toNat = y.toNat → y.toNat ≥ x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x = y → x ≤ y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_of_eq | [198, 11] | [199, 31] | exact Nat.le_of_eq | x y : Pos
⊢ x.toNat = y.toNat → y.toNat ≥ x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x.toNat = y.toNat → y.toNat ≥ x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_of_lt | [201, 11] | [202, 31] | by_toNat | x y : Pos
⊢ x < y → x ≤ y | x y : Pos
⊢ y.toNat > x.toNat → y.toNat ≥ x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x < y → x ≤ y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_of_lt | [201, 11] | [202, 31] | exact Nat.le_of_lt | x y : Pos
⊢ y.toNat > x.toNat → y.toNat ≥ x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ y.toNat > x.toNat → y.toNat ≥ x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.ne_of_lt | [204, 11] | [205, 31] | by_toNat | x y : Pos
⊢ x < y → x ≠ y | x y : Pos
⊢ y.toNat > x.toNat → x.toNat ≠ y.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x < y → x ≠ y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.ne_of_lt | [204, 11] | [205, 31] | exact Nat.ne_of_lt | x y : Pos
⊢ y.toNat > x.toNat → x.toNat ≠ y.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ y.toNat > x.toNat → x.toNat ≠ y.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_of_le_of_ne | [207, 11] | [208, 37] | by_toNat | x y : Pos
⊢ x ≤ y → x ≠ y → x < y | x y : Pos
⊢ y.toNat ≥ x.toNat → x.toNat ≠ y.toNat → y.toNat > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x ≤ y → x ≠ y → x < y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_of_le_of_ne | [207, 11] | [208, 37] | exact Nat.lt_of_le_of_ne | x y : Pos
⊢ y.toNat ≥ x.toNat → x.toNat ≠ y.toNat → y.toNat > x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ y.toNat ≥ x.toNat → x.toNat ≠ y.toNat → y.toNat > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_of_not_gt | [210, 11] | [211, 35] | by_toNat | x y : Pos
⊢ ¬x > y → x ≤ y | x y : Pos
⊢ ¬x.toNat > y.toNat → y.toNat ≥ x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ ¬x > y → x ≤ y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_of_not_gt | [210, 11] | [211, 35] | exact Nat.le_of_not_gt | x y : Pos
⊢ ¬x.toNat > y.toNat → y.toNat ≥ x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ ¬x.toNat > y.toNat → y.toNat ≥ x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_of_not_ge | [213, 11] | [214, 35] | by_toNat | x y : Pos
⊢ ¬x ≥ y → x < y | x y : Pos
⊢ ¬x.toNat ≥ y.toNat → y.toNat > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ ¬x ≥ y → x < y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_of_not_ge | [213, 11] | [214, 35] | exact Nat.gt_of_not_le | x y : Pos
⊢ ¬x.toNat ≥ y.toNat → y.toNat > x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ ¬x.toNat ≥ y.toNat → y.toNat > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_le_of_gt | [216, 11] | [217, 35] | by_toNat | x y : Pos
⊢ x > y → ¬x ≤ y | x y : Pos
⊢ x.toNat > y.toNat → ¬y.toNat ≥ x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x > y → ¬x ≤ y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_le_of_gt | [216, 11] | [217, 35] | exact Nat.not_le_of_gt | x y : Pos
⊢ x.toNat > y.toNat → ¬y.toNat ≥ x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x.toNat > y.toNat → ¬y.toNat ≥ x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_lt_of_ge | [219, 11] | [220, 35] | by_toNat | x y : Pos
⊢ x ≥ y → ¬x < y | x y : Pos
⊢ x.toNat ≥ y.toNat → ¬y.toNat > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x ≥ y → ¬x < y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_lt_of_ge | [219, 11] | [220, 35] | exact Nat.not_lt_of_ge | x y : Pos
⊢ x.toNat ≥ y.toNat → ¬y.toNat > x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x.toNat ≥ y.toNat → ¬y.toNat > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.eq_or_lt_of_le | [234, 11] | [235, 37] | by_toNat | x y : Pos
⊢ x ≤ y → x = y ∨ x < y | x y : Pos
⊢ y.toNat ≥ x.toNat → x.toNat = y.toNat ∨ y.toNat > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x ≤ y → x = y ∨ x < y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.eq_or_lt_of_le | [234, 11] | [235, 37] | exact Nat.eq_or_lt_of_le | x y : Pos
⊢ y.toNat ≥ x.toNat → x.toNat = y.toNat ∨ y.toNat > x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ y.toNat ≥ x.toNat → x.toNat = y.toNat ∨ y.toNat > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_or_ge | [240, 11] | [241, 34] | by_toNat | x y : Pos
⊢ x < y ∨ x ≥ y | x y : Pos
⊢ y.toNat > x.toNat ∨ x.toNat ≥ y.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x < y ∨ x ≥ y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_or_ge | [240, 11] | [241, 34] | exact Nat.lt_or_ge .. | x y : Pos
⊢ y.toNat > x.toNat ∨ x.toNat ≥ y.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ y.toNat > x.toNat ∨ x.toNat ≥ y.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.one_le | [243, 11] | [244, 57] | by_toNat | x : Pos
⊢ 1 ≤ x | x : Pos
⊢ x.toNat ≥ 1 | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ 1 ≤ x
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.one_le | [243, 11] | [244, 57] | apply Nat.succ_le_of_lt | x : Pos
⊢ x.toNat ≥ 1 | case h
x : Pos
⊢ 0 < x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x.toNat ≥ 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.one_le | [243, 11] | [244, 57] | exact Nat.zero_lt _ | case h
x : Pos
⊢ 0 < x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h
x : Pos
⊢ 0 < x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_lt_one | [246, 11] | [247, 100] | by_toNat | x : Pos
⊢ ¬x < 1 | x : Pos
⊢ ¬1 > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬x < 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_lt_one | [246, 11] | [247, 100] | intro h | x : Pos
⊢ ¬1 > x.toNat | x : Pos
h : 1 > x.toNat
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬1 > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_lt_one | [246, 11] | [247, 100] | absurd h | x : Pos
h : 1 > x.toNat
⊢ False | x : Pos
h : 1 > x.toNat
⊢ ¬1 > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
h : 1 > x.toNat
⊢ False
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_lt_one | [246, 11] | [247, 100] | apply Nat.not_lt_of_ge | x : Pos
h : 1 > x.toNat
⊢ ¬1 > x.toNat | case a
x : Pos
h : 1 > x.toNat
⊢ x.toNat ≥ 1 | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
h : 1 > x.toNat
⊢ ¬1 > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_lt_one | [246, 11] | [247, 100] | apply Nat.succ_le_of_lt | case a
x : Pos
h : 1 > x.toNat
⊢ x.toNat ≥ 1 | case a.h
x : Pos
h : 1 > x.toNat
⊢ 0 < x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
case a
x : Pos
h : 1 > x.toNat
⊢ x.toNat ≥ 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_lt_one | [246, 11] | [247, 100] | exact Nat.zero_lt _ | case a.h
x : Pos
h : 1 > x.toNat
⊢ 0 < x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a.h
x : Pos
h : 1 > x.toNat
⊢ 0 < x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.one_lt_succ | [249, 11] | [250, 56] | by_toNat | x : Pos
⊢ 1 < x + 1 | x : Pos
⊢ x.toNat + 1 > 1 | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ 1 < x + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.one_lt_succ | [249, 11] | [250, 56] | apply Nat.succ_lt_succ | x : Pos
⊢ x.toNat + 1 > 1 | case a
x : Pos
⊢ 0 < x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x.toNat + 1 > 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.one_lt_succ | [249, 11] | [250, 56] | exact Nat.zero_lt _ | case a
x : Pos
⊢ 0 < x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
x : Pos
⊢ 0 < x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_le_one | [252, 11] | [253, 99] | by_toNat | x : Pos
⊢ ¬x + 1 ≤ 1 | x : Pos
⊢ ¬1 ≥ x.toNat + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬x + 1 ≤ 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_le_one | [252, 11] | [253, 99] | intro h | x : Pos
⊢ ¬1 ≥ x.toNat + 1 | x : Pos
h : 1 ≥ x.toNat + 1
⊢ False | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬1 ≥ x.toNat + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_le_one | [252, 11] | [253, 99] | absurd h | x : Pos
h : 1 ≥ x.toNat + 1
⊢ False | x : Pos
h : 1 ≥ x.toNat + 1
⊢ ¬1 ≥ x.toNat + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
h : 1 ≥ x.toNat + 1
⊢ False
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_le_one | [252, 11] | [253, 99] | apply Nat.not_le_of_gt | x : Pos
h : 1 ≥ x.toNat + 1
⊢ ¬1 ≥ x.toNat + 1 | case h
x : Pos
h : 1 ≥ x.toNat + 1
⊢ x.toNat + 1 > 1 | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
h : 1 ≥ x.toNat + 1
⊢ ¬1 ≥ x.toNat + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_le_one | [252, 11] | [253, 99] | apply Nat.succ_lt_succ | case h
x : Pos
h : 1 ≥ x.toNat + 1
⊢ x.toNat + 1 > 1 | case h.a
x : Pos
h : 1 ≥ x.toNat + 1
⊢ 0 < x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
case h
x : Pos
h : 1 ≥ x.toNat + 1
⊢ x.toNat + 1 > 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_le_one | [252, 11] | [253, 99] | exact Nat.zero_lt _ | case h.a
x : Pos
h : 1 ≥ x.toNat + 1
⊢ 0 < x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case h.a
x : Pos
h : 1 ≥ x.toNat + 1
⊢ 0 < x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_succ_self | [258, 11] | [259, 38] | by_toNat | x : Pos
⊢ x ≤ x + 1 | x : Pos
⊢ x.toNat + 1 ≥ x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x ≤ x + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_succ_self | [258, 11] | [259, 38] | exact Nat.le_add_right .. | x : Pos
⊢ x.toNat + 1 ≥ x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x.toNat + 1 ≥ x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_succ_self | [261, 11] | [262, 38] | by_toNat | x : Pos
⊢ x < x + 1 | x : Pos
⊢ x.toNat + 1 > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x < x + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_succ_self | [261, 11] | [262, 38] | exact Nat.lt_succ_self .. | x : Pos
⊢ x.toNat + 1 > x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ x.toNat + 1 > x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_le_self | [264, 11] | [265, 41] | by_toNat | x : Pos
⊢ ¬x + 1 ≤ x | x : Pos
⊢ ¬x.toNat ≥ x.toNat + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬x + 1 ≤ x
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_le_self | [264, 11] | [265, 41] | exact Nat.not_succ_le_self _ | x : Pos
⊢ ¬x.toNat ≥ x.toNat + 1 | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬x.toNat ≥ x.toNat + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_lt_self | [267, 11] | [268, 62] | by_toNat | x : Pos
⊢ ¬x + 1 < x | x : Pos
⊢ ¬x.toNat > x.toNat + 1 | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬x + 1 < x
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_lt_self | [267, 11] | [268, 62] | apply Nat.not_lt_of_ge | x : Pos
⊢ ¬x.toNat > x.toNat + 1 | case a
x : Pos
⊢ x.toNat + 1 ≥ x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x : Pos
⊢ ¬x.toNat > x.toNat + 1
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.not_succ_lt_self | [267, 11] | [268, 62] | exact Nat.le_add_right .. | case a
x : Pos
⊢ x.toNat + 1 ≥ x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case a
x : Pos
⊢ x.toNat + 1 ≥ x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_of_lt_succ | [270, 11] | [271, 36] | by_toNat | x y : Pos
⊢ x < y + 1 → x ≤ y | x y : Pos
⊢ y.toNat + 1 > x.toNat → y.toNat ≥ x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x < y + 1 → x ≤ y
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.le_of_lt_succ | [270, 11] | [271, 36] | exact Nat.le_of_lt_succ | x y : Pos
⊢ y.toNat + 1 > x.toNat → y.toNat ≥ x.toNat | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ y.toNat + 1 > x.toNat → y.toNat ≥ x.toNat
TACTIC:
|
https://github.com/fgdorais/extra4.git | eb1c6c30f5790bed1bb4b01534d271a2490d9730 | Extra/Pos/Lemmas.lean | Pos.lt_succ_of_le | [273, 11] | [274, 36] | by_toNat | x y : Pos
⊢ x ≤ y → x < y + 1 | x y : Pos
⊢ y.toNat ≥ x.toNat → y.toNat + 1 > x.toNat | Please generate a tactic in lean4 to solve the state.
STATE:
x y : Pos
⊢ x ≤ y → x < y + 1
TACTIC:
|
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