27 lines
800 B
Text
27 lines
800 B
Text
open nat
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-- deeper congruence
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universe l
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constants (T : Type.{l}) (x1 x2 x3 x4 x5 x6 : T) (f : T → T → T)
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constants (f_comm : ∀ x y, f x y = f y x)
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(f_l : ∀ x y z, f (f x y) z = f x (f y z))
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(f_r : ∀ x y z, f x (f y z) = f y (f x z))
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namespace tst
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attribute f_comm [simp]
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attribute f_l [simp]
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attribute f_r [simp]
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end tst
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#simplify eq tst 0 (f (f x2 x4) (f x5 (f x3 (f x1 x6))))
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open is_trunc
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constants g : Π (x y : nat), x ≠ y → Type₁
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constants a b c : nat
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constants H₁ : a ≠ b
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constants H₂ : a = c
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namespace tst attribute H₂ [simp] end tst
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definition ne_is_hprop [instance] (a b : nat) : is_hprop (a ≠ b) :=
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sorry
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-- TODO(Daniel): simplifier seems to have applied unnecessary step (see: (eq.nrec ... (eq.refl ..)))
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#simplify eq tst 0 (g a b H₁)
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