[STATEMENT]
lemma bet2_lt_le__lt:
  assumes "Bet a Po b" and
    "Bet A PO B" and
    "Cong Po a PO A" and
    "Po b Lt PO B"
  shows "a b Lt A B"
[PROOF STATE]
proof (prove)
goal (1 subgoal):
 1. a b Lt A B
[PROOF STEP]
by (smt Lt_def Tarski_neutral_dimensionless.l4_3_1 Tarski_neutral_dimensionless_axioms assms(1) assms(2) assms(3) assms(4) bet2_le2__le cong__le not_cong_2143)