30 lines
1.2 KiB
Text
30 lines
1.2 KiB
Text
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--- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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--- Released under Apache 2.0 license as described in the file LICENSE.
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--- Author: Jeremy Avigad
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----------------------------------------------------------------------------------------------------
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import logic data.nat
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using nat
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namespace simp
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-- first define a class of homogeneous equality
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inductive simplifies_to {T : Type} (t1 t2 : T) : Prop :=
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| mk : t1 = t2 → simplifies_to t1 t2
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theorem get_eq {T : Type} {t1 t2 : T} (C : simplifies_to t1 t2) : t1 = t2 :=
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simplifies_to_rec (λx, x) C
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theorem infer_eq {T : Type} (t1 t2 : T) {C : simplifies_to t1 t2} : t1 = t2 :=
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simplifies_to_rec (λx, x) C
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theorem simp_app [instance] (S : Type) (T : Type) (f1 f2 : S → T) (s1 s2 : S)
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(C1 : simplifies_to f1 f2) (C2 : simplifies_to s1 s2) : simplifies_to (f1 s1) (f2 s2) :=
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mk (congr (get_eq C1) (get_eq C2))
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theorem test1 (S : Type) (T : Type) (f1 f2 : S → T) (s1 s2 : S) (Hf : f1 = f2) (Hs : s1 = s2) :
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f1 s1 = f2 s2 :=
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have Rs [fact] : simplifies_to f1 f2, from mk Hf,
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have Cs [fact] : simplifies_to s1 s2, from mk Hs,
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infer_eq _ _
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