(* Properties on degree assignment for terms ********************************)
fact da_cpr_lpr_aux: ∀h,g,G0,L0,T0.
- (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_snv_lsstas h g G1 L1 T1) →
+ (∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_snv_lstas h g G1 L1 T1) →
(∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_snv_cpr_lpr h g G1 L1 T1) →
(∀G1,L1,T1. ⦃G0, L0, T0⦄ >≡[h, g] ⦃G1, L1, T1⦄ → IH_da_cpr_lpr h g G1 L1 T1) →
∀G1,L1,T1. G0 = G1 → L0 = L1 → T0 = T1 → IH_da_cpr_lpr h g G1 L1 T1.
lapply (da_inv_bind … Hl) -Hl #Hl
elim (cpds_inv_abst1 … HT10) -HT10 #W3 #U3 #HW3 #_ #H destruct -U3
lapply (cprs_div … HW3 … HW10) -W3 #HWW1
- lapply (ssta_da_conf … HVW1 … Hl0) <minus_plus_m_m #H
+ lapply (da_sta_conf … HVW1 … Hl0) <minus_plus_m_m #H
elim (snv_fwd_da … HW) #l1 #Hl1
- lapply (IH3 … HV1 … 1 … Hl0 W1 ?) /2 width=2 by fqup_fpbg, ssta_lsstas/ #HW1
+ lapply (IH3 … HV1 … 1 … Hl0 W1 ?) /2 width=2 by fqup_fpbg, sta_lstas/ #HW1
lapply (da_cpcs_aux … IH2 IH1 … Hl1 … H … HWW1) -H
- /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, ssta_fpbs/ #H destruct
+ /3 width=5 by fpbg_fpbs_trans, fqup_fpbg, sta_fpbs/ #H destruct
lapply (IH1 … HV1 … Hl0 … HV12 … HL12) -HV1 -Hl0 -HV12 [ /2 by fqup_fpbg/ ] #Hl0
lapply (IH1 … Hl1 … HW2 … HL12) -Hl1 // /2 width=1 by fqup_fpbg/ -HW
lapply (IH1 … HU1 … Hl … HU12 (L2.ⓛW2) ?) -IH1 -HU1 -Hl -HU12 [1,2: /2 by fqup_fpbg, lpr_pair/ ] -HL12 -HW2