(* Properties concerning stratified native validity *************************)
fact snv_lsubsv_aux: ∀h,g,L0,T0.
- (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ltpr_tpr h g L1 T1) →
- (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_ltpr_tpr h g L1 T1) →
+ (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_cpr_lpr h g L1 T1) →
+ (∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_ssta_cpr_lpr h g L1 T1) →
(∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_ssta h g L1 T1) →
(∀L1,T1. h ⊢ ⦃L0, T0⦄ >[g] ⦃L1, T1⦄ → IH_snv_lsubsv h g L1 T1) →
∀L1,T1. L0 = L1 → T0 = T1 → IH_snv_lsubsv h g L1 T1.
[ #i #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
elim (snv_inv_lref … H) -H #I2 #K2 #W2 #HLK2 #HW2
elim (lsubsv_ldrop_O1_trans … HL12 … HLK2) -HL12 #X #H #HLK1
- lapply (ldrop_pair2_fwd_fw … HLK2 (#i)) -HLK2 #HLK2
elim (lsubsv_inv_pair2 … H) -H * #K1
- [ #HK12 #H destruct /4 width=8 by snv_lref, fw_ygt/ (**) (* auto too slow without trace *)
+ [ #HK12 #H destruct
+ /5 width=8 by snv_lref, fsupp_ygt, fsupp_lref/ (**) (* auto too slow without trace *)
| #W1 #V1 #V2 #l #HV1 #_ #_ #_ #_ #_ #H #_ destruct /2 width=5/
]
| #p #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2 -IH1
lapply (lsubsv_cprs_trans … HL12 … HW0) -HW0 #HW0
elim (lsubsv_ssta_trans … HVW … HL12) -HVW #W1 #HVW1 #HW1
lapply (cpcs_cprs_strap1 … HW1 … HW0) -W #HW10
- elim (dxprs_lsubsv_aux … IH4 IH3 IH2 IH1 … HL12 … HTU) -IH4 -IH3 -IH2 -HTU // /2 width=1/ #X #HTU #H
- elim (cprs_inv_abst1 Abst W0 … H) -H #W #U2 #HW0 #HU2 #H destruct
+ elim (lsubsv_dxprs_aux … IH4 IH3 IH2 IH1 … HL12 … HTU) -IH4 -IH3 -IH2 -HTU // /2 width=1/ #X #HTU #H
+ elim (cprs_fwd_abst1 … H Abst W0) -H #W #U2 #HW0 #HU2 #H destruct
lapply (cpcs_cprs_strap1 … HW10 … HW0) -W0 #H
elim (cpcs_inv_cprs … H) -H #W0 #HW10 #HW0
lapply (dxprs_cprs_trans … (ⓛ{a}W0.U2) HTU ?) [ /2 width=1/ ] -HTU -HW0
- /4 width=8 by snv_appl, fw_ygt/ (**) (* auto too slow without trace *)
+ /4 width=8 by snv_appl, fsupp_ygt/ (**) (* auto too slow without trace *)
| #W #T #HL0 #HT0 #H #L1 #HL12 destruct -IH4 -IH3 -IH2
elim (snv_inv_cast … H) -H #U #l #HW #HT #HTU #HUW
lapply (lsubsv_cpcs_trans … HL12 … HUW) -HUW #HUW
elim (lsubsv_ssta_trans … HTU … HL12) -HTU #U0 #HTU0 #HU0
- lapply (cpcs_trans … HU0 … HUW) -U /4 width=4 by snv_cast, fw_ygt/ (**) (* auto too slow without trace *)
+ lapply (cpcs_trans … HU0 … HUW) -U /4 width=4 by snv_cast, fsupp_ygt/ (**) (* auto too slow without trace *)
]
qed-.