(* 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_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, 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_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.
#h #g #G0 #L0 #T0 #IH3 #IH2 #IH1 #G1 #L1 * * [|||| * ]
[ #k #_ #_ #_ #_ #l #H2 #X3 #H3 #L2 #_ -IH3 -IH2 -IH1
lapply (fqup_lref … G1 … HLK1)
elim (lpr_ldrop_conf … HLK1 … HL12) -HLK1 -HL12 #X #H #HLK2
elim (lpr_inv_pair1 … H) -H #K2 #V2 #HK12 #_ #H destruct
- lapply (ldrop_fwd_ldrop2 … HLK2) -V2
+ lapply (ldrop_fwd_drop2 … HLK2) -V2
/4 width=7 by da_lift, fqup_fpbg/
]
| #p #_ #_ #HT0 #H1 destruct -IH3 -IH2 -IH1
[ #V2 #T2 #HV12 #HT12 #H destruct
/4 width=9 by da_bind, fqup_fpbg, lpr_pair/
| #T2 #HT12 #HT2 #H1 #H2 destruct
- /4 width=11 by da_inv_lift, fqup_fpbg, lpr_pair, ldrop_ldrop/
+ /4 width=11 by da_inv_lift, fqup_fpbg, lpr_pair, ldrop_drop/
]
| #V1 #T1 #HG0 #HL0 #HT0 #H1 #l #H2 #X3 #H3 #L2 #HL12 destruct
elim (snv_inv_appl … H1) -H1 #b0 #W1 #W0 #T0 #l0 #HV1 #HT1 #Hl0 #HVW1 #HW10 #HT10