definition twice ≝ λn.\ 5a href="cic:/matita/tutorial/chapter2/add.fix(0,0,1)"\ 6add\ 5/a\ 6 n n.
-(* We are interested to prove that for any natural number m there exists a natural number m that
-is the integer half of m. This will give us the opportunity to introduce new connectives and
+(* We are interested to prove that for any natural number n there exists a natural number m that
+is the integer half of n. This will give us the opportunity to introduce new connectives and
quantifiers and, later on, to make some interesting consideration on proofs and computations. *)
theorem ex_half: ∀n.\ 5a title="exists" href="cic:/fakeuri.def(1)"\ 6∃\ 5/a\ 6m. n \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a href="cic:/matita/tutorial/chapter2/twice.def(2)"\ 6twice\ 5/a\ 6 m \ 5a title="logical or" href="cic:/fakeuri.def(1)"\ 6∨\ 5/a\ 6 n \ 5a title="leibnitz's equality" href="cic:/fakeuri.def(1)"\ 6=\ 5/a\ 6 \ 5a href="cic:/matita/tutorial/chapter2/nat.con(0,2,0)"\ 6S\ 5/a\ 6 (\ 5a href="cic:/matita/tutorial/chapter2/twice.def(2)"\ 6twice\ 5/a\ 6 m).