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);
[1: exists [apply something] intro n; cases (PU n);
split; intros; try split;[apply H1;|apply H2] assumption;
|2: intros 2 (x Hx); cases Hx; cases H1; clear H1;
- cases (PU 〈(fst x),x1〉); lapply (H4 H2) as H5; simplify in H5;
- cases (PU 〈x1,(snd x)〉); lapply (H7 H3) as H8; simplify in H8;
+ cases (PU 〈(\fst x),x1〉); lapply (H4 H2) as H5; simplify in H5;
+ cases (PU 〈x1,(\snd x)〉); lapply (H7 H3) as H8; simplify in H8;
generalize in match H5; generalize in match H8;
generalize in match (PU x); clear H6 H7 H1 H4 H2 H3 H5 H8;
cases x; simplify; intros; cases H1; clear H1; apply H4;