notation "hvbox(\langle term 19 a, break term 19 b\rangle)"
with precedence 90 for @{ 'pair $a $b}.
+notation "hvbox(〈term 19 a, break term 19 b〉)"
+with precedence 90 for @{ 'pair $a $b}.
notation "hvbox(x break \times y)" with precedence 70
for @{ 'product $x $y}.
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 *)