Definition pairN : Type := (N * N).Definition pred_double_correct' : ltac:(auto_for_auto pred_double_correct) := pred_double_correct.Definition succ_double_mask_correct' : ltac:(auto_for_auto succ_double_mask_correct) := succ_double_mask_correct.Definition double_mask_correct' : ltac:(auto_for_auto double_mask_correct) := double_mask_correct.Definition double_pred_mask_correct' : ltac:(auto_for_auto double_pred_mask_correct) := double_pred_mask_correct.Definition sub_mask_correct' : ltac:(auto_for_auto sub_mask_correct) := sub_mask_correct.Definition compare_cont_correct' : ltac:(auto_for_auto compare_cont_correct) := compare_cont_correct.Definition compare_correct' : ltac:(auto_for_auto compare_correct) := compare_correct.Definition succ_double_correct' : ltac:(auto_for_auto succ_double_correct) := succ_double_correct.Definition double_correct' : ltac:(auto_for_auto double_correct) := double_correct.Definition sub_correct' : ltac:(auto_for_auto sub_correct) := sub_correct.Definition compare0_correct' : ltac:(auto_for_auto compare0_correct) := compare0_correct.Definition leb_aux_correct' : ltac:(auto_for_auto leb_aux_correct) := leb_aux_correct.Definition leb_correct' : ltac:(auto_for_auto leb_correct) := leb_correct.Definition cond_correct' A : ltac:(auto_for_auto (@cond_correct A)) := cond_correct.Definition mod_aux_correct' : ltac:(auto_for_auto mod_aux_correct) := mod_aux_correct.

Lemma mod_0 n : n mod 0 = n.