alias symbol "pi2" = "pair pi2".
alias symbol "pi1" = "pair pi1".
alias symbol "and" = "logical and".
- apply (∃_:unit.∀n:C square.(\fst n ≈ \snd n → P n) ∧ (P n → \fst n ≈ \snd n));
+ apply (∃d:unit.∀n:C square.(\fst n ≈ \snd n → P n) ∧ (P n → \fst n ≈ \snd n));
|2: intros 4 (U H x Hx); simplify in Hx;
cases H (_ H1); cases (H1 x); apply H2; apply Hx;
|3: intros; cases H (_ PU); cases H1 (_ PV);