+fact cnv_cpms_conf_lpr_refl_step_aux (a) (h) (o) (G0) (L0) (T0) (m21) (m22):
+ (∀G,L,T. ⦃G0,L0,T0⦄ >[h,o] ⦃G,L,T⦄ → IH_cnv_cpm_trans_lpr a h G L T) →
+ (∀G,L,T. ⦃G0,L0,T0⦄ >[h,o] ⦃G,L,T⦄ → IH_cnv_cpms_conf_lpr a h G L T) →
+ ⦃G0,L0⦄ ⊢ T0 ![a,h] →
+ ∀X2. ⦃G0,L0⦄ ⊢ T0 ➡[m21,h] X2 → (T0 ≛[h,o] X2 → ⊥) → ∀T2. ⦃G0,L0⦄ ⊢ X2 ➡*[m22,h] T2 →
+ ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
+ ∃∃T. ⦃G0,L1⦄ ⊢ T0 ➡*[m21+m22,h] T& ⦃G0,L2⦄ ⊢ T2 ➡*[h] T.
+#a #h #o #G0 #L0 #T0 #m21 #m22 #IH2 #IH1 #H0
+#X2 #HX02 #HnX02 #T2 #HXT2
+#L1 #HL01 #L2 #HL02
+lapply (cnv_cpm_trans_lpr_aux … IH1 IH2 … HX02 … L0 ?) // #HX2
+elim (cnv_cpm_conf_lpr_aux … IH2 IH1 … HX02 … 0 T0 … L0 … HL01) //
+<minus_n_O <minus_O_n #Y1 #HXY1 #HTY1
+elim (cnv_cpms_strip_lpr_sub … IH1 … HXT2 0 X2 … HL02 L0) [|*: /4 width=2 by fpb_fpbg, cpm_fpb/ ]
+<minus_n_O <minus_O_n #Y2 #HTY2 #HXY2 -HXT2
+elim (IH1 … HXY1 … HXY2 … HL01 … HL02) [|*: /4 width=2 by fpb_fpbg, cpm_fpb/ ]
+-a -o -L0 -X2 <minus_n_O <minus_O_n #Y #HY1 #HY2
+lapply (cpms_trans … HTY1 … HY1) -Y1 #HT0Y
+lapply (cpms_trans … HTY2 … HY2) -Y2 #HT2Y
+/2 width=3 by ex2_intro/
+qed-.