- @cpce_zero_drops #n #p #Y1 #X1 #V1 #U1 #HLY1 #HWU1
- lapply (drops_mono … HLY1 … HLK1) -L1 #H2 destruct
- /4 width=12 by lpr_cpms_trans, cpms_step_sn/
- | #Y0 #W0 #W1 #HLY0 #HW01 #HWX1 -HI -HW0 -IH
- lapply (drops_mono … HLY0 … HLK0) -HLY0 #H destruct
- @(ex2_intro … X1) [| /2 width=6 by cpm_delta_drops/ ]
+ @(cpce_ldec_drops … HLK1) -HLK1 #n #p #V0 #U0 #HWU0
+ /4 width=10 by lpr_cpms_trans, cpms_step_sn/
+ | #n #p #W01 #W02 #V0 #V01 #V02 #U0 #H1 #HWU0 #HW001 #HW012 #HV001 #HV012 #H2 destruct
+ ]
+ | lapply (drops_isuni_fwd_drop2 … HLK1) [ // ] -W1 #HLK1
+ #Y0 #X0 #W1 #HLY0 #HW01 #HWX1 -HL01 -HL02
+ lapply (drops_mono … HLY0 … HLK0) -HLY0 #H destruct
+ lapply (cpce_inv_lref_sn_drops_ldef … HX2 … HLK0) -HX2 #H destruct
+ elim (IH … HW0 … HW01 … HW02 … HK01 … HK02)
+ [| /3 width=2 by fqup_fpbg, fqup_lref/ ] -L0 -K0 #W #HW1 #HW2
+ elim (lifts_total W (𝐔❴↑i❵)) #V #HWV
+ /3 width=9 by cpce_lifts_bi, cpm_delta_drops, ex2_intro/
+ | lapply (drops_isuni_fwd_drop2 … HLK1) [ // ] -W1 #HLK1
+ #m #Y0 #X0 #W1 #HLY0 #HW01 #HWX1 #H destruct -HL01 -HL02
+ lapply (drops_mono … HLY0 … HLK0) -HLY0 #H destruct
+ elim (cpce_inv_lref_sn_drops_ldec … HX2 … HLK0) -HX2 *
+ [ #_ #H destruct
+ elim (IH … HW0 … HW01 … HW02 … HK01 … HK02)
+ [| /3 width=2 by fqup_fpbg, fqup_lref/ ] -L0 -K0 #W #HW1 #HW2
+ elim (lifts_total W (𝐔❴↑i❵)) #V #HWV
+ /3 width=9 by cpce_lifts_bi, cpm_ell_drops, ex2_intro/
+ | lapply (drops_isuni_fwd_drop2 … HLK2) [ // ] -W2 #HLK2
+ #n #p #W01 #W02 #V0 #V01 #V02 #U0 #_ #HW001 #HW012 #_ #_ #H destruct -V0 -V01 -U0
+ elim (IH … HW0 … HW01 … HW001 … HK01 … HK02)
+ [| /3 width=2 by fqup_fpbg, fqup_lref/ ] -L0 -K0 #W #HW1 #HW2
+ elim (lifts_total W (𝐔❴↑i❵)) #V #HWV
+ /4 width=11 by cpce_lifts_bi, cpm_lifts_bi, cpm_ee, ex2_intro/
+ ]
+ ]
+| #l #_ #_ #n #X1 #HX1 #X2 #HX2 #L1 #HL01 #L2 #HL02
+ elim (cpm_inv_gref1 … HX1) -HX1 #H1 #H2 destruct
+ lapply (cpce_inv_gref_sn … HX2) -HX2 #H destruct
+ /3 width=3 by cpce_gref, cpr_refl, ex2_intro/