rewrite > (H4 ?); [2: reflexivity]
apply le_to_le_to_eq;
[1: apply os_le_to_nat_le;
- apply (trans_increasing ? H ? ? (nat_le_to_os_le ?? H5));
+ apply (trans_increasing a H ? ? (nat_le_to_os_le ?? H5));
|2: apply (trans_le ? x ?);[apply os_le_to_nat_le; apply (H2 j);]
rewrite < (H4 ?); [2: reflexivity] apply le_n;]
qed.
change in H1:(? ? ? %) with (\fst b);
change in a with (hos_carr (half_segment_ordered_set ? s));
change in b with (hos_carr (half_segment_ordered_set ? s));
- apply rule H1;
+ apply rule (x2sx_ ? s ?? H1);
| right; change in H1:(? ? % ?) with (\fst b);
change in H1:(? ? ? %) with (\fst a);
change in a with (hos_carr (half_segment_ordered_set ? s));
change in b with (hos_carr (half_segment_ordered_set ? s));
- apply rule H1;]
+ apply rule (x2sx_ ? s ?? H1);]
qed.
|7:apply (ge_reflexive (l : hos_carr (os_r C)));
|8:apply (H12 i);
|6:change with (a i ≤ a (m O));
- apply (trans_decreasing ? H6 (\fst (m 0)) i); intro; apply (le_to_not_lt ?? H4 H16);]]
+ apply (trans_decreasing a H6 (\fst (m 0)) i); intro; apply (le_to_not_lt ?? H4 H16);]]
clear H10; intros (p q r); change with (w p 〈a (m q),a (m r)〉);
generalize in match (refl_eq nat (m p));
generalize in match (m p) in ⊢ (? ? ? % → %); intro X; cases X (w1 H15); clear X;