cut (\fst w2 = O); [2: clear H10;
symmetry; apply le_n_O_to_eq; rewrite > (sum_bases_O l1 (\fst w2)); [apply le_n]
apply (q_le_trans ??? H9); rewrite < H4; rewrite > q_d_x_x;
- left; reflexivity;]
+ apply q_eq_to_le; reflexivity;]
rewrite > Hcut; clear Hcut H10 H9; simplify in H5 H6;
cut (ⅆ[input,init] = Qpos w) as E; [2:
rewrite > H2; rewrite < H4; rewrite > q_d_sym;
- rewrite > q_d_noabs; [reflexivity] right; assumption;]
+ rewrite > q_d_noabs; [reflexivity] apply q_lt_to_le; assumption;]
cases (\fst w1) in H5 H6; intros;
[1: cases (?:False); clear H5; simplify in H6;
apply (q_lt_corefl ⅆ[input,init]);
apply q_le_minus_r; rewrite < q_minus_r;
rewrite < E in ⊢ (??%); assumption;]
|2: intros; rewrite > H8; rewrite > H7; clear H8 H7;
- simplify in H5 H6 ⊢ %;
- simplify in H5:(? ? (? ? %));
+ simplify in H5 H6 ⊢ %;
+ cases (\fst w1) in H5 H6; [intros; reflexivity]
+ cases (bars l1);
+ [1: intros; simplify; elim n [reflexivity] simplify; assumption;
+ |2: simplify; intros; cases (?:False);
-
+STOP
alias symbol "pi2" = "pair pi2".
alias symbol "pi1" = "pair pi1".