proposition: Lemma i_j_j_i : forall i j a : E, create i j a = create j i a.
proof: Proof. ir. unfold create in |- *. apply by_cases with (a = i). ir. ap (Y_if H). sy. apply by_cases with (a = j). ir. ap (Y_if H0). rewrite <- H. am. ir. ap (Y_if_not H0). sy. ap (Y_if H). tv. ir. ap (Y_if_not H). apply by_cases with (a = j). ir. ap (Y_if H0). sy. ap (Y_if H0). tv. ir. ap (Y_if_not H0). ap (Y_if_not H0). ap (Y_if_not H). tv. Qed.
imports: tactics