interpretation "pair pi2" 'pi2b x y = (snd ? ? x y).
theorem eq_pair_fst_snd: ∀A,B.∀p:A \ 5a title="Product" href="cic:/fakeuri.def(1)"\ 6×\ 5/a\ 6 B.
- p \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a title="Pair construction" href="cic:/fakeuri.def(1)"\ 6〈\ 5/a\ 6 \ 5a title="pair pi1" href="cic:/fakeuri.def(1)"\ 6\fst\ 5/a\ 6 p, \ 5a title="pair pi2" href="cic:/fakeuri.def(1)"\ 6\snd\ 5/a\ 6 p 〉.
+ p \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a title="Pair construction" href="cic:/fakeuri.def(1)"\ 6〈\ 5/a\ 6 \ 5a title="pair pi1" href="cic:/fakeuri.def(1)"\ 6\fst\ 5/a\ 6 p, \ 5a title="pair pi2" href="cic:/fakeuri.def(1)"\ 6\snd\ 5/a\ 6 p 〉.
#A #B #p (cases p) // qed.
(* sum *)
inductive Sig (A:Type[0]) (f:A→Type[0]) : Type[0] ≝
dp: ∀a:A.(f a)→Sig A f.
-interpretation "Sigma" 'sigma x = (Sig ? x).
+interpretation "Sigma" 'sigma x = (Sig ? x).
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