A \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 B \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 C \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 A \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 (B \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 C).
#S #A #B #C #w % [* [* /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ | /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ ] | * [/\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ | * /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/]
qed.
A \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 B \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 C \ 5a title="extensional equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 61 A \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 (B \ 5a title="union" href="cic:/fakeuri.def(1)"\ 6∪\ 5/a\ 6 C).
#S #A #B #C #w % [* [* /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ | /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ ] | * [/\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/ | * /\ 5span class="autotactic"\ 63\ 5span class="autotrace"\ 6 trace \ 5a href="cic:/matita/basics/logic/Or.con(0,1,2)"\ 6or_introl\ 5/a\ 6, \ 5a href="cic:/matita/basics/logic/Or.con(0,2,2)"\ 6or_intror\ 5/a\ 6\ 5/span\ 6\ 5/span\ 6/]
qed.