(λn.fst (a n)) ↑ x → a ↑ (sig_in ?? x h).
intros; cases H (Ha Hx); split [apply Ha] cases Hx;
split; [apply H1] intros;
(λn.fst (a n)) ↑ x → a ↑ (sig_in ?? x h).
intros; cases H (Ha Hx); split [apply Ha] cases Hx;
split; [apply H1] intros;
(λn.fst (a n)) ↓ x → a ↓ (sig_in ?? x h).
intros; cases H (Ha Hx); split [apply Ha] cases Hx;
split; [apply H1] intros;
(λn.fst (a n)) ↓ x → a ↓ (sig_in ?? x h).
intros; cases H (Ha Hx); split [apply Ha] cases Hx;
split; [apply H1] intros;
apply (H (λx:{[l,u]} square.U 〈fst (fst x),fst (snd x)〉));
(unfold segment_ordered_uniform_space; simplify);
exists [apply U] split; [assumption;]
apply (H (λx:{[l,u]} square.U 〈fst (fst x),fst (snd x)〉));
(unfold segment_ordered_uniform_space; simplify);
exists [apply U] split; [assumption;]