Definition same_except_cur (m m' : Mem.mem) :=
Mem.mem_contents m = Mem.mem_contents m' /\
max_access_at m = max_access_at m' /\
Mem.nextblock m = Mem.nextblock m'.

Lemma mem_cohere_same_except_cur m m' phi :
same_except_cur m m' ->
mem_cohere' m phi ->
mem_cohere' m' phi.