34 lines
989 B
Text
34 lines
989 B
Text
open tactic
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constants (A : Type) (rel : A → A → Prop)
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(rel.refl : ∀ a, rel a a)
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(rel.symm : ∀ a b, rel a b → rel b a)
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(rel.trans : ∀ a b c, rel a b → rel b c → rel a c)
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attribute [refl] rel.refl
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attribute [symm] rel.symm
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attribute [trans] rel.trans
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constants (x y z : A) (f g h : A → A)
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(H₁ : rel (f x) (g y))
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(H₂ : rel (h (g y)) z)
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(Hf : ∀ (a b : A), rel a b → rel (f a) (f b))
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(Hg : ∀ (a b : A), rel a b → rel (g a) (g b))
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(Hh : ∀ (a b : A), rel a b → rel (h a) (h b))
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attribute [simp] H₁ H₂
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attribute [congr] Hf Hg Hh
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#print [simp] default
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#print [congr] default
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meta definition relsimp_core (e : expr) : tactic (expr × expr) :=
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do S ← simp_lemmas.mk_default,
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e_type ← infer_type e >>= whnf,
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simplify S [] e {} `rel
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example : rel (h (f x)) z :=
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by do e₁ ← to_expr ```(h (f x)),
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(e₁', pf) ← relsimp_core e₁,
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exact pf
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