lean2/tests/lean/hott/subst_tac.hlean

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open nat
example (A B : Type) (a : A) (b : B) (h₁ : A = B) (h₂ : eq.rec_on h₁ a = b) : b = eq.rec_on h₁ a :=
begin
subst h₁ h₂
end
example (A B : Type) (a : A) (b : B) (h₁ : A = B) (h₂ : eq.rec_on h₁ a = b) : b = eq.rec_on h₁ a :=
begin
subst B h₂
end
example (a b c : nat) (a0 : a = 0) (b1 : b = 1 + a) (ab : a = b) : empty :=
begin
subst a0,
subst b1,
contradiction
end
example (a : nat) : a = 0 → a = 1 → empty :=
begin
intro a0 a1,
subst a0,
contradiction
end
example (a b c : nat) : a = 0 → b = 1 + a → a = b → empty :=
begin
intro a0 b1 ab,
subst a0,
rewrite b1 at *,
state,
contradiction
end
example (a b c : nat) : a = 0 → b = 1 + a → a = b → empty :=
begin
intro a0 b1 ab,
subst a0, subst b1,
state,
contradiction
end
example (a b c : nat) : a = 0 → 1 + a = b → a = b → empty :=
begin
intro a0 b1 ab,
subst a0 b1,
state,
contradiction
end
example (a b c : nat) : a = 0 → 1 + a = b → a = b → empty :=
begin
intros,
subst a b,
state,
contradiction
end