(* A on yk:= (A_1 m k y0): *)

Lemma A_B_1_B_yk :
forall(m:fmap)(k:dim)(x0 y0:dart),
inv_qhmap m ->
exd m x0 -> exd m y0 -> y0 <> A m k x0 ->
A (B_1 (B m k x0) k y0) k (A_1 m k y0) = nil.