Datasets:
pkuAI4M
/
lean_github

Dataset card Data Studio Files
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 Community
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https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_add
[96, 1]
[101, 34]
{ rfl }
case zero a : MyNat ⊢ succ a + 0 = succ (a + 0) case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ succ a + 0 = succ (a + 0) case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_add
[96, 1]
[101, 34]
{ rw [add_succ, add_succ, hd] }
case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_add
[96, 1]
[101, 34]
rfl
case zero a : MyNat ⊢ succ a + 0 = succ (a + 0)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ succ a + 0 = succ (a + 0) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_add
[96, 1]
[101, 34]
rw [add_succ, add_succ, hd]
case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_comm
[104, 1]
[112, 18]
induction' b with d hd
a b : MyNat ⊢ a + b = b + a
case zero a : MyNat ⊢ a + 0 = 0 + a case succ a d : MyNat hd : a + d = d + a ⊢ a + succ d = succ d + a
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat ⊢ a + b = b + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [add_zero]
case zero a : MyNat ⊢ a + 0 = 0 + a
case zero a : MyNat ⊢ a = 0 + a
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ a + 0 = 0 + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [zero_add]
case zero a : MyNat ⊢ a = 0 + a
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ a = 0 + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [add_succ]
case succ a d : MyNat hd : a + d = d + a ⊢ a + succ d = succ d + a
case succ a d : MyNat hd : a + d = d + a ⊢ succ (a + d) = succ d + a
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : a + d = d + a ⊢ a + succ d = succ d + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [hd]
case succ a d : MyNat hd : a + d = d + a ⊢ succ (a + d) = succ d + a
case succ a d : MyNat hd : a + d = d + a ⊢ succ (d + a) = succ d + a
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : a + d = d + a ⊢ succ (a + d) = succ d + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [succ_add]
case succ a d : MyNat hd : a + d = d + a ⊢ succ (d + a) = succ d + a
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : a + d = d + a ⊢ succ (d + a) = succ d + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_assoc
[116, 1]
[120, 8]
induction' c with d hd
a b c : MyNat ⊢ a + b + c = a + (b + c)
case zero a b : MyNat ⊢ a + b + 0 = a + (b + 0) case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ a + b + succ d = a + (b + succ d)
Please generate a tactic in lean4 to solve the state. STATE: a b c : MyNat ⊢ a + b + c = a + (b + c) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_assoc
[116, 1]
[120, 8]
rfl
case zero a b : MyNat ⊢ a + b + 0 = a + (b + 0)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero a b : MyNat ⊢ a + b + 0 = a + (b + 0) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_assoc
[116, 1]
[120, 8]
rw [add_succ, hd]
case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ a + b + succ d = a + (b + succ d)
case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ succ (a + (b + d)) = a + (b + succ d)
Please generate a tactic in lean4 to solve the state. STATE: case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ a + b + succ d = a + (b + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_assoc
[116, 1]
[120, 8]
rfl
case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ succ (a + (b + d)) = a + (b + succ d)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ succ (a + (b + d)) = a + (b + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_add_add
[130, 1]
[131, 8]
sorry
a b c d : MyNat ⊢ a + b + (c + d) = a + c + (b + d)
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b c d : MyNat ⊢ a + b + (c + d) = a + c + (b + d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.is_zero_zero_eq_True
[141, 1]
[142, 6]
rfl
⊢ is_zero 0 = True
no goals
Please generate a tactic in lean4 to solve the state. STATE: ⊢ is_zero 0 = True TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.is_zero_succ_eq_False
[144, 1]
[145, 6]
rfl
n : MyNat ⊢ is_zero (succ n) = False
no goals
Please generate a tactic in lean4 to solve the state. STATE: n : MyNat ⊢ is_zero (succ n) = False TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
intro h
⊢ 0 ≠ 1
h : 0 = 1 ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: ⊢ 0 ≠ 1 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
rw [← is_zero_one_eq_False]
h : 0 = 1 ⊢ False
h : 0 = 1 ⊢ is_zero 1
Please generate a tactic in lean4 to solve the state. STATE: h : 0 = 1 ⊢ False TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
rw [← h]
h : 0 = 1 ⊢ is_zero 1
h : 0 = 1 ⊢ is_zero 0
Please generate a tactic in lean4 to solve the state. STATE: h : 0 = 1 ⊢ is_zero 1 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
rw [is_zero_zero_eq_True]
h : 0 = 1 ⊢ is_zero 0
h : 0 = 1 ⊢ True
Please generate a tactic in lean4 to solve the state. STATE: h : 0 = 1 ⊢ is_zero 0 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
trivial
h : 0 = 1 ⊢ True
no goals
Please generate a tactic in lean4 to solve the state. STATE: h : 0 = 1 ⊢ True TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.pred_succ
[165, 1]
[166, 6]
rfl
a : MyNat ⊢ pred (succ a) = a
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ pred (succ a) = a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_inj
[168, 1]
[172, 9]
suffices h : pred (succ a) = pred (succ b) by { rw [pred_succ, pred_succ] at h exact h }
a b : MyNat h : succ a = succ b ⊢ a = b
a b : MyNat h : succ a = succ b ⊢ pred (succ a) = pred (succ b)
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat h : succ a = succ b ⊢ a = b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_inj
[168, 1]
[172, 9]
rw [h]
a b : MyNat h : succ a = succ b ⊢ pred (succ a) = pred (succ b)
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat h : succ a = succ b ⊢ pred (succ a) = pred (succ b) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_inj
[168, 1]
[172, 9]
rw [pred_succ, pred_succ] at h
a b : MyNat h✝ : succ a = succ b h : pred (succ a) = pred (succ b) ⊢ a = b
a b : MyNat h✝ : succ a = succ b h : a = b ⊢ a = b
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat h✝ : succ a = succ b h : pred (succ a) = pred (succ b) ⊢ a = b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_inj
[168, 1]
[172, 9]
exact h
a b : MyNat h✝ : succ a = succ b h : a = b ⊢ a = b
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat h✝ : succ a = succ b h : a = b ⊢ a = b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.zero_mul
[190, 1]
[191, 8]
sorry
a : MyNat ⊢ 0 * a = 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ 0 * a = 0 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_eq_add_one
[193, 1]
[194, 8]
sorry
a : MyNat ⊢ succ a = a + 1
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ succ a = a + 1 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.mul_one
[196, 1]
[197, 8]
sorry
a : MyNat ⊢ a * 1 = a
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ a * 1 = a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.one_mul
[199, 1]
[200, 8]
sorry
a : MyNat ⊢ one * a = a
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ one * a = a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.succ_mul
[202, 1]
[203, 8]
sorry
a b : MyNat ⊢ succ a * b = a * b + b
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat ⊢ succ a * b = a * b + b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.mul_add
[205, 1]
[206, 8]
sorry
t a b : MyNat ⊢ t * (a + b) = t * a + t * b
no goals
Please generate a tactic in lean4 to solve the state. STATE: t a b : MyNat ⊢ t * (a + b) = t * a + t * b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.mul_assoc
[208, 1]
[209, 8]
sorry
a b c : MyNat ⊢ a * b * c = a * (b * c)
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b c : MyNat ⊢ a * b * c = a * (b * c) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.add_mul
[214, 1]
[215, 8]
sorry
a b t : MyNat ⊢ (a + b) * t = a * t + b * t
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b t : MyNat ⊢ (a + b) * t = a * t + b * t TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulSolutions.lean
MyNat.mul_comm
[217, 1]
[218, 8]
sorry
a b : MyNat ⊢ a * b = b * a
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat ⊢ a * b = b * a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NumberTheory5Solutions.lean
sixteen_pow_sixtyfour_mod_nineteen
[31, 1]
[32, 6]
rfl
⊢ 16 ^ 64 = 16
no goals
Please generate a tactic in lean4 to solve the state. STATE: ⊢ 16 ^ 64 = 16 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_zero
[59, 1]
[60, 6]
rfl
n : MyNat ⊢ n + 0 = n
no goals
Please generate a tactic in lean4 to solve the state. STATE: n : MyNat ⊢ n + 0 = n TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_succ
[63, 1]
[64, 6]
rfl
n m : MyNat ⊢ n + succ m = succ (n + m)
no goals
Please generate a tactic in lean4 to solve the state. STATE: n m : MyNat ⊢ n + succ m = succ (n + m) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.easy
[69, 1]
[70, 6]
rfl
⊢ two + two = four
no goals
Please generate a tactic in lean4 to solve the state. STATE: ⊢ two + two = four TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.easy2
[73, 1]
[74, 6]
rfl
⊢ two + one = one + two
no goals
Please generate a tactic in lean4 to solve the state. STATE: ⊢ two + one = one + two TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_add
[88, 1]
[92, 14]
induction' n with d hd
n : MyNat ⊢ 0 + n = n
case zero ⊢ 0 + 0 = 0 case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d
Please generate a tactic in lean4 to solve the state. STATE: n : MyNat ⊢ 0 + n = n TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_add
[88, 1]
[92, 14]
{ rfl }
case zero ⊢ 0 + 0 = 0 case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d
case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d
Please generate a tactic in lean4 to solve the state. STATE: case zero ⊢ 0 + 0 = 0 case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_add
[88, 1]
[92, 14]
{ rw [add_succ] rw [hd] }
case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_add
[88, 1]
[92, 14]
rfl
case zero ⊢ 0 + 0 = 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero ⊢ 0 + 0 = 0 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_add
[88, 1]
[92, 14]
rw [add_succ]
case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d
case succ d : MyNat hd : 0 + d = d ⊢ succ (0 + d) = succ d
Please generate a tactic in lean4 to solve the state. STATE: case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_add
[88, 1]
[92, 14]
rw [hd]
case succ d : MyNat hd : 0 + d = d ⊢ succ (0 + d) = succ d
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ d : MyNat hd : 0 + d = d ⊢ succ (0 + d) = succ d TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_add
[96, 1]
[101, 34]
induction' b with d hd
a b : MyNat ⊢ succ a + b = succ (a + b)
case zero a : MyNat ⊢ succ a + 0 = succ (a + 0) case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat ⊢ succ a + b = succ (a + b) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_add
[96, 1]
[101, 34]
{ rfl }
case zero a : MyNat ⊢ succ a + 0 = succ (a + 0) case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ succ a + 0 = succ (a + 0) case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_add
[96, 1]
[101, 34]
{ rw [add_succ, add_succ, hd] }
case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_add
[96, 1]
[101, 34]
rfl
case zero a : MyNat ⊢ succ a + 0 = succ (a + 0)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ succ a + 0 = succ (a + 0) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_add
[96, 1]
[101, 34]
rw [add_succ, add_succ, hd]
case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_comm
[104, 1]
[112, 18]
induction' b with d hd
a b : MyNat ⊢ a + b = b + a
case zero a : MyNat ⊢ a + 0 = 0 + a case succ a d : MyNat hd : a + d = d + a ⊢ a + succ d = succ d + a
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat ⊢ a + b = b + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [add_zero]
case zero a : MyNat ⊢ a + 0 = 0 + a
case zero a : MyNat ⊢ a = 0 + a
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ a + 0 = 0 + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [zero_add]
case zero a : MyNat ⊢ a = 0 + a
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ a = 0 + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [add_succ]
case succ a d : MyNat hd : a + d = d + a ⊢ a + succ d = succ d + a
case succ a d : MyNat hd : a + d = d + a ⊢ succ (a + d) = succ d + a
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : a + d = d + a ⊢ a + succ d = succ d + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [hd]
case succ a d : MyNat hd : a + d = d + a ⊢ succ (a + d) = succ d + a
case succ a d : MyNat hd : a + d = d + a ⊢ succ (d + a) = succ d + a
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : a + d = d + a ⊢ succ (a + d) = succ d + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_comm
[104, 1]
[112, 18]
rw [succ_add]
case succ a d : MyNat hd : a + d = d + a ⊢ succ (d + a) = succ d + a
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : a + d = d + a ⊢ succ (d + a) = succ d + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_assoc
[116, 1]
[120, 8]
induction' c with d hd
a b c : MyNat ⊢ a + b + c = a + (b + c)
case zero a b : MyNat ⊢ a + b + 0 = a + (b + 0) case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ a + b + succ d = a + (b + succ d)
Please generate a tactic in lean4 to solve the state. STATE: a b c : MyNat ⊢ a + b + c = a + (b + c) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_assoc
[116, 1]
[120, 8]
rfl
case zero a b : MyNat ⊢ a + b + 0 = a + (b + 0)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero a b : MyNat ⊢ a + b + 0 = a + (b + 0) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_assoc
[116, 1]
[120, 8]
rw [add_succ, hd]
case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ a + b + succ d = a + (b + succ d)
case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ succ (a + (b + d)) = a + (b + succ d)
Please generate a tactic in lean4 to solve the state. STATE: case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ a + b + succ d = a + (b + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_assoc
[116, 1]
[120, 8]
rfl
case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ succ (a + (b + d)) = a + (b + succ d)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ succ (a + (b + d)) = a + (b + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_add_add
[130, 1]
[131, 8]
sorry
a b c d : MyNat ⊢ a + b + (c + d) = a + c + (b + d)
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b c d : MyNat ⊢ a + b + (c + d) = a + c + (b + d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.is_zero_zero_eq_True
[141, 1]
[142, 6]
rfl
⊢ is_zero 0 = True
no goals
Please generate a tactic in lean4 to solve the state. STATE: ⊢ is_zero 0 = True TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.is_zero_succ_eq_False
[144, 1]
[145, 6]
rfl
n : MyNat ⊢ is_zero (succ n) = False
no goals
Please generate a tactic in lean4 to solve the state. STATE: n : MyNat ⊢ is_zero (succ n) = False TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
intro h
⊢ 0 ≠ 1
h : 0 = 1 ⊢ False
Please generate a tactic in lean4 to solve the state. STATE: ⊢ 0 ≠ 1 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
rw [← is_zero_one_eq_False]
h : 0 = 1 ⊢ False
h : 0 = 1 ⊢ is_zero 1
Please generate a tactic in lean4 to solve the state. STATE: h : 0 = 1 ⊢ False TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
rw [← h]
h : 0 = 1 ⊢ is_zero 1
h : 0 = 1 ⊢ is_zero 0
Please generate a tactic in lean4 to solve the state. STATE: h : 0 = 1 ⊢ is_zero 1 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
rw [is_zero_zero_eq_True]
h : 0 = 1 ⊢ is_zero 0
h : 0 = 1 ⊢ True
Please generate a tactic in lean4 to solve the state. STATE: h : 0 = 1 ⊢ is_zero 0 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_ne_one
[151, 1]
[156, 10]
trivial
h : 0 = 1 ⊢ True
no goals
Please generate a tactic in lean4 to solve the state. STATE: h : 0 = 1 ⊢ True TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.pred_succ
[165, 1]
[166, 6]
rfl
a : MyNat ⊢ pred (succ a) = a
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ pred (succ a) = a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_inj
[168, 1]
[172, 9]
suffices h : pred (succ a) = pred (succ b) by { rw [pred_succ, pred_succ] at h exact h }
a b : MyNat h : succ a = succ b ⊢ a = b
a b : MyNat h : succ a = succ b ⊢ pred (succ a) = pred (succ b)
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat h : succ a = succ b ⊢ a = b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_inj
[168, 1]
[172, 9]
rw [h]
a b : MyNat h : succ a = succ b ⊢ pred (succ a) = pred (succ b)
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat h : succ a = succ b ⊢ pred (succ a) = pred (succ b) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_inj
[168, 1]
[172, 9]
rw [pred_succ, pred_succ] at h
a b : MyNat h✝ : succ a = succ b h : pred (succ a) = pred (succ b) ⊢ a = b
a b : MyNat h✝ : succ a = succ b h : a = b ⊢ a = b
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat h✝ : succ a = succ b h : pred (succ a) = pred (succ b) ⊢ a = b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_inj
[168, 1]
[172, 9]
exact h
a b : MyNat h✝ : succ a = succ b h : a = b ⊢ a = b
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat h✝ : succ a = succ b h : a = b ⊢ a = b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.zero_mul
[190, 1]
[191, 8]
sorry
a : MyNat ⊢ 0 * a = 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ 0 * a = 0 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_eq_add_one
[193, 1]
[194, 8]
sorry
a : MyNat ⊢ succ a = a + 1
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ succ a = a + 1 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.mul_one
[196, 1]
[197, 8]
sorry
a : MyNat ⊢ a * 1 = a
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ a * 1 = a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.one_mul
[199, 1]
[200, 8]
sorry
a : MyNat ⊢ one * a = a
no goals
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ one * a = a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.succ_mul
[202, 1]
[203, 8]
sorry
a b : MyNat ⊢ succ a * b = a * b + b
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat ⊢ succ a * b = a * b + b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.mul_add
[205, 1]
[206, 8]
sorry
t a b : MyNat ⊢ t * (a + b) = t * a + t * b
no goals
Please generate a tactic in lean4 to solve the state. STATE: t a b : MyNat ⊢ t * (a + b) = t * a + t * b TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.mul_assoc
[208, 1]
[209, 8]
sorry
a b c : MyNat ⊢ a * b * c = a * (b * c)
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b c : MyNat ⊢ a * b * c = a * (b * c) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.add_mul
[214, 1]
[215, 8]
sorry
a b t : MyNat ⊢ (a + b) * t = a * t + b * t
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b t : MyNat ⊢ (a + b) * t = a * t + b * t TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NatAddMul.lean
MyNat.mul_comm
[217, 1]
[218, 8]
sorry
a b : MyNat ⊢ a * b = b * a
no goals
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat ⊢ a * b = b * a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NumberTheory5.lean
sixteen_pow_sixtyfour_mod_nineteen
[31, 1]
[32, 6]
rfl
⊢ 16 ^ 64 = 16
no goals
Please generate a tactic in lean4 to solve the state. STATE: ⊢ 16 ^ 64 = 16 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NumberTheory3.lean
arb_large_soln
[31, 1]
[32, 8]
sorry
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1
no goals
Please generate a tactic in lean4 to solve the state. STATE: ⊢ ∀ (N : ℕ), ∃ n, n > N ∧ 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NumberTheory3.lean
infinite_iff_arb_large
[39, 1]
[40, 8]
sorry
S : Set ℕ ⊢ Set.Infinite S ↔ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S
no goals
Please generate a tactic in lean4 to solve the state. STATE: S : Set ℕ ⊢ Set.Infinite S ↔ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ S TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NumberTheory3.lean
infinite_set_of_solutions
[44, 1]
[46, 23]
rw [infinite_iff_arb_large]
⊢ Set.Infinite { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 }
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 }
Please generate a tactic in lean4 to solve the state. STATE: ⊢ Set.Infinite { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 } TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/NumberTheory3.lean
infinite_set_of_solutions
[44, 1]
[46, 23]
exact arb_large_soln
⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 }
no goals
Please generate a tactic in lean4 to solve the state. STATE: ⊢ ∀ (N : ℕ), ∃ n, n > N ∧ n ∈ { n | 5 ∣ 4 * n ^ 2 + 1 ∧ 13 ∣ 4 * n ^ 2 + 1 } TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.zero_add
[31, 1]
[34, 22]
induction' a using MyNat.induction with d hd
a : MyNat ⊢ 0 + a = a
case zero ⊢ 0 + 0 = 0 case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d
Please generate a tactic in lean4 to solve the state. STATE: a : MyNat ⊢ 0 + a = a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.zero_add
[31, 1]
[34, 22]
rw [add_zero]
case zero ⊢ 0 + 0 = 0
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero ⊢ 0 + 0 = 0 TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.zero_add
[31, 1]
[34, 22]
rw [add_succ, hd]
case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ d : MyNat hd : 0 + d = d ⊢ 0 + succ d = succ d TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.succ_add
[36, 1]
[39, 32]
induction' b using MyNat.induction with d hd
a b : MyNat ⊢ succ a + b = succ (a + b)
case zero a : MyNat ⊢ succ a + 0 = succ (a + 0) case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat ⊢ succ a + b = succ (a + b) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.succ_add
[36, 1]
[39, 32]
rw [add_zero, add_zero]
case zero a : MyNat ⊢ succ a + 0 = succ (a + 0)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ succ a + 0 = succ (a + 0) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.succ_add
[36, 1]
[39, 32]
rw [add_succ, add_succ, hd]
case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : succ a + d = succ (a + d) ⊢ succ a + succ d = succ (a + succ d) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.add_comm
[41, 1]
[44, 32]
induction' b using MyNat.induction with d hd
a b : MyNat ⊢ a + b = b + a
case zero a : MyNat ⊢ a + 0 = 0 + a case succ a d : MyNat hd : a + d = d + a ⊢ a + succ d = succ d + a
Please generate a tactic in lean4 to solve the state. STATE: a b : MyNat ⊢ a + b = b + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.add_comm
[41, 1]
[44, 32]
rw [add_zero, zero_add]
case zero a : MyNat ⊢ a + 0 = 0 + a
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero a : MyNat ⊢ a + 0 = 0 + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.add_comm
[41, 1]
[44, 32]
rw [add_succ, succ_add, hd]
case succ a d : MyNat hd : a + d = d + a ⊢ a + succ d = succ d + a
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ a d : MyNat hd : a + d = d + a ⊢ a + succ d = succ d + a TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.add_assoc
[46, 1]
[49, 42]
induction' c using MyNat.induction with d hd
a b c : MyNat ⊢ a + b + c = a + (b + c)
case zero a b : MyNat ⊢ a + b + 0 = a + (b + 0) case succ a b d : MyNat hd : a + b + d = a + (b + d) ⊢ a + b + succ d = a + (b + succ d)
Please generate a tactic in lean4 to solve the state. STATE: a b c : MyNat ⊢ a + b + c = a + (b + c) TACTIC:
https://github.com/kbuzzard/IISc-experiments.git
f2f2d7d14b3ec1957fcdd38cc0e3657df6850047
IIScExperiments/Solutions/NatAddMulExperiments.lean
MyNat.add_assoc
[46, 1]
[49, 42]
rw [add_zero, add_zero]
case zero a b : MyNat ⊢ a + b + 0 = a + (b + 0)
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero a b : MyNat ⊢ a + b + 0 = a + (b + 0) TACTIC: