2015-11-05 05:53:12 +00:00
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/- Basic rewriting with a custom relation without congruence or conditionals -/
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import logic.connectives data.nat
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universe l
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constant T : Type.{l}
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2015-11-16 19:01:53 +00:00
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constants (x y z : T) (f g h : T → T)
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constants (R : T → T → Prop)
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2015-11-05 05:53:12 +00:00
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constants (R_refl : ∀ x, R x x) (R_sym : ∀ x y, R x y → R y x) (R_trans : ∀ x y z, R x y → R y z → R x z)
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constants (Hfxgy : R (f x) (g y)) (Hgyhz : R (g y) (h z))
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2015-11-16 19:01:53 +00:00
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namespace tst attribute R_refl [refl] end tst
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namespace tst attribute R_sym [symm] end tst
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#simplify R tst 2 (f x) -- f x
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namespace tst attribute R_trans [trans] end tst
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#simplify R tst 2 (f x) -- f x
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namespace tst attribute Hfxgy [simp] end tst
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#simplify R tst 2 (f x) -- f x
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namespace tst attribute Hgyhz [simp] end tst
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#simplify R tst 2 (f x) -- f x
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