58 lines
1.8 KiB
Text
58 lines
1.8 KiB
Text
open tactic
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example (a b : nat) (s t : list nat) : a::s = b::t → a ≠ b → false :=
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by cc
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example (a b : nat) (s t : list nat) : a::s = b::t → t ≠ s → false :=
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by cc
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example (a c b : nat) (s t : list nat) : a::s = b::t → a ≠ c → c = b → false :=
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by cc
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example (a c b : nat) (s t : list nat) : a::a::s = a::b::t → a ≠ c → c = b → false :=
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by cc
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example (a b : nat) (s t r : list nat) : a::s = r → r = b::t → a ≠ b → false :=
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by cc
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example (a b : nat) (s t r : list nat) : a::s = r → r = b::t → a = b :=
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by cc
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example (a b : nat) (s t r : list nat) : list.cons a = list.cons b → a = b :=
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begin
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intro h1,
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/- In the current implementation, cc does not "complete" partially applied
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constructor applications. So, the following one should fail. -/
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try {cc},
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/- Complete it manually. TODO(Leo): we can automate it for inhabited types. -/
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note h := congr_fun h1 [],
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cc
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end
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inductive foo
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| mk1 : nat → nat → foo
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| mk2 : nat → nat → foo
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example (a b : nat) : foo.mk1 a = foo.mk2 b → false :=
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begin
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intro h1,
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/- In the current implementation, cc does not "complete" partially applied
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constructor applications. So, the following one should fail. -/
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try {cc},
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note h := congr_fun h1 0,
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cc
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end
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universe variables u
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inductive Vec (α : Type u) : nat → Type (max 1 u)
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| nil : Vec 0
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| cons : ∀ {n}, α → Vec n → Vec (nat.succ n)
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example (α : Type u) (a b c d : α) (n : nat) (s t : Vec α n) : Vec.cons a s = Vec.cons b t → a ≠ b → false :=
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by cc
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example (α : Type u) (a b c d : α) (n : nat) (s t : Vec α n) : Vec.cons a s = Vec.cons b t → t ≠ s → false :=
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by cc
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example (α : Type u) (a b c d : α) (n : nat) (s t : Vec α n) : Vec.cons a (Vec.cons a s) = Vec.cons a (Vec.cons b t) → b ≠ c → c = a → false :=
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by cc
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