16711fcdba
TODO for `dsimp`: - Add an option for reducing [reducible] definitions - Add (to_unfold : list name) similar to the one in the `simp` tactic
53 lines
1.3 KiB
Text
53 lines
1.3 KiB
Text
open smt_tactic tactic
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lemma ex1 (a b c : nat) : a = c → a = b → b = c :=
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by using_smt intros
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set_option pp.all true
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lemma ex2 (a b c : nat) : a > nat.zero → a = c → a = b → b = c :=
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by using_smt intros
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lemma ex3 (p q r : Prop) : p → q → ¬p → r :=
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by using_smt intros
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lemma ex4 (a b c : nat) : a > nat.zero → 0 < a :=
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by simp [(>)]; using_smt intros
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lemma ex5 (a b c d : nat) : a ≠ d → a = b ∧ b = c → a = c :=
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by using_smt intros
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set_option pp.all false
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lemma ex6 (f : nat → nat) (a b c : nat) :
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f a = 0 →
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f b = 1 →
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f a = f b ∨ f a = c →
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c = 0 :=
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by using_smt intros
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lemma ex7 (f : nat → nat) (a b c d e: nat) :
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f a = 0 →
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f a = d →
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f b = e →
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f b = 1 →
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d = e ∨ f a = c →
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c = 0 :=
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by using_smt intros
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lemma ex8 (f : bool → bool) (a b c : bool) :
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f a = ff →
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f b = tt →
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f a = f b ∨ f a = c →
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c = ff :=
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by using_smt intros
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lemma ex9 (f : list nat → list nat) (a b c : list nat) :
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f a = [] →
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f b = [0, 1] →
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f a = f b ∨ f a = c →
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c = [] :=
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by using_smt intros
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lemma ex10 (a b c d e : int) : a = b → b ≠ c → (a = c ∨ d = e) → d = e :=
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by using_smt intros
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