lean4-htt/tests/lean/run/1202.lean
2022-08-11 07:16:38 -07:00

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opaque f : Bool → Bool → Bool
axiom f_comm (a b : Bool) : f a b = f b a
axiom f_assoc (a b c : Bool) : f (f a b) c = f a (f b c)
instance : Lean.IsCommutative f := ⟨f_comm⟩
instance : Lean.IsAssociative f := ⟨f_assoc⟩
example (a b c : Bool) : f (f a b) c = f (f a c) b :=
by ac_rfl -- good
example (a b c : Bool) : (f (f a b) c = f (f a c) b) ∧ true :=
And.intro (by ac_rfl) rfl -- good
example (a b c : Bool) : (f (f a b) c = f (f a c) b) ∧ true := by
apply And.intro
. ac_rfl
. rfl