lean2/tests/lean/congr1.lean
Leonardo de Moura 9aaa2d0991 feat(frontends/lean): add new command for testing new congruence lemmas
Remark: #congr_simp is the old command, and #congr is the new one.
2015-11-12 18:55:25 -08:00

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import data.list
#congr_simp @add
#congr_simp @ite
#congr_simp @perm
section
variables p : nat → Prop
variables q : nat → nat → Prop
variables f : Π (x y : nat), p x → q x y → nat
#congr_simp f
end
constant p : Π {A : Type}, A → Prop
constant q : Π {A : Type} (n m : A), p n → p m → Prop
constant r : Π {A : Type} (n m : A) (H₁ : p n) (H₂ : p m), q n m H₁ H₂ → Prop
constant h : Π (A : Type) (n m : A)
(H₁ : p n) (H₂ : p m) (H₃ : q n n H₁ H₁) (H₄ : q n m H₁ H₂)
(H₅ : r n m H₁ H₂ H₄) (H₆ : r n n H₁ H₁ H₃), A
#congr_simp h