74 lines
2.1 KiB
Text
74 lines
2.1 KiB
Text
open tactic
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set_option pp.implicit true
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example (a b c d : nat) (f : nat → nat → nat) : a = b → b = c → d + (if b > 0 then a else b) = 0 → f (b + b) b ≠ f (a + c) c → false :=
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by do intros,
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s ← cc_state.mk_using_hs,
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trace s,
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t₁ ← to_expr `(f (b + b) b),
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t₂ ← to_expr `(f (a + c) c),
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b ← to_expr `(b),
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d ← to_expr `(d),
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guard (s^.inconsistent),
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guard (s^.eqc_size b = 4),
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guard (not (s^.in_singlenton_eqc b)),
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guard (s^.in_singlenton_eqc d),
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trace ">>> Equivalence roots",
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trace s^.roots,
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trace ">>> b's equivalence class",
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trace (s^.eqc_of b),
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pr ← s^.eqv_proof t₁ t₂,
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note `h pr,
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contradiction
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example (a b : nat) (f : nat → nat) : a = b → f a = f b :=
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by cc
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example (a b : nat) (f : nat → nat) : a = b → f a ≠ f b → false :=
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by cc
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example (a b : nat) (f : nat → nat) : a = b → f (f a) ≠ f (f b) → false :=
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by cc
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example (a b c : nat) (f : nat → nat) : a = b → c = b → f (f a) ≠ f (f c) → false :=
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by cc
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example (a b c : nat) (f : nat → nat → nat) : a = b → c = b → f (f a b) a ≠ f (f c c) c → false :=
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by cc
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example (a b c : nat) (f : nat → nat → nat) : a = b → c = b → f (f a b) a = f (f c c) c :=
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by cc
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example (a b c d : nat) : a == b → b = c → c == d → a == d :=
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by cc
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example (a b c d : nat) : a = b → b = c → c == d → a == d :=
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by cc
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example (a b c d : nat) : a = b → b == c → c == d → a == d :=
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by cc
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example (a b c d : nat) : a == b → b == c → c = d → a == d :=
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by cc
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example (a b c d : nat) : a == b → b = c → c = d → a == d :=
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by cc
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example (a b c d : nat) : a = b → b = c → c = d → a == d :=
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by cc
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example (a b c d : nat) : a = b → b == c → c = d → a == d :=
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by cc
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constant f {α : Type} : α → α → α
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constant g : nat → nat
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example (a b c : nat) : a = b → g a == g b :=
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by cc
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example (a b c : nat) : a = b → c = b → f (f a b) (g c) = f (f c a) (g b) :=
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by cc
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example (a b c d e x y : nat) : a = b → a = x → b = y → c = d → c = e → c = b → a = e :=
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by cc
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