2014-02-04 21:53:30 +00:00
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variables A B : (Type U)
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variables t1 t2 : A ⨯ B
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2014-02-10 17:03:42 +00:00
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axiom pair_Ax {A : (Type U)} {B : A → (Type U)} (p : sig x, B x) : (pair (proj1 p) (proj2 p) : sig x, B x) = p
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2014-02-04 21:53:30 +00:00
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theorem spairext {A B : (Type U)} {p1 p2 : A ⨯ B} (H1 : proj1 p1 = proj1 p2) (H2 : proj2 p1 = proj2 p2) : p1 = p2
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2014-02-10 17:03:42 +00:00
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:= calc p1 = (pair (proj1 p1) (proj2 p1)) : symm (pair_Ax p1)
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... = (pair (proj1 p2) (proj2 p1)) : { H1 }
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... = (pair (proj1 p2) (proj2 p2)) : { H2 }
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2014-02-04 21:53:30 +00:00
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... = p2 : pair_Ax p2
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