2014-02-02 23:01:48 +00:00
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import heq
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2014-01-25 05:25:09 +00:00
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variable vec : Nat → Type
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variable concat {n m : Nat} (v : vec n) (w : vec m) : vec (n + m)
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infixl 65 ; : concat
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axiom concat_assoc {n1 n2 n3 : Nat} (v1 : vec n1) (v2 : vec n2) (v3 : vec n3) :
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(v1 ; v2) ; v3 = cast (congr2 vec (symm (Nat::add_assoc n1 n2 n3)))
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(v1 ; (v2 ; v3))
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variable empty : vec 0
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axiom concat_empty {n : Nat} (v : vec n) :
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v ; empty = cast (congr2 vec (symm (Nat::add_zeror n)))
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v
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rewrite_set simple
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add_rewrite concat_assoc concat_empty Nat::add_assoc Nat::add_zeror and_truer eq_id : simple
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variable n : Nat
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variable v : vec n
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variable w : vec n
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variable f {A : TypeM} : A → A
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variable p {A : TypeM} : A → Bool
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axiom fax {n m : Nat} (v : vec n) (w : vec m) : f (v; (w; v)) = v; (w; v)
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add_rewrite fax : simple
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(*
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local t = parse_lean([[ p (f ((v ; w) ; empty ; (v ; empty))) ∧ v = cast (congr2 vec (Nat::add_zeror n)) (v ; empty) ]])
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print(t)
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print("===>")
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local t2, pr = simplify(t, "simple")
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print(t2)
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print("checking proof")
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print (get_environment():type_check(pr))
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*)
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