[STATEMENT]
lemma measure_to_qbs_cong_sets:
  assumes "sets M = sets N"
  shows "measure_to_qbs M = measure_to_qbs N"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. measure_to_qbs M = measure_to_qbs N
[PROOF STEP]
by(rule qbs_eqI) (simp add: measurable_cong_sets[OF _ assms])