(* Properties with context-sensitive free variables *************************)
(* Note: "⦃L2, T1⦄ ⊆ ⦃L0, T1⦄" may not hold *)
-axiom cpx_lfxs_conf_fle: ∀R. c_reflexive … R →
- ∀h,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
+axiom cpx_lfxs_conf_fle: ∀R,h. c_reflexive … R →
+ (∨∨ (∀G. (cpx h G) = R) | R_fle_compatible R) →
+ ∀G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈[h] T1 →
∀L2. L0 ⪤*[R, T0] L2 →
∧∧ ⦃L2, T0⦄ ⊆ ⦃L0, T0⦄ & ⦃L2, T1⦄ ⊆ ⦃L2, T0⦄
& ⦃L0, T1⦄ ⊆ ⦃L0, T0⦄.
(*
-#R #HR #h #G #L0 #T0 @(fqup_wf_ind_eq (Ⓕ) … G L0 T0) -G -L0 -T0
+#R #h #H1R #H2R #G #L0 #T0 @(fqup_wf_ind_eq (Ⓕ) … G L0 T0) -G -L0 -T0
#G #L #T #IH #G0 #L0 * *
[ #s #HG #HL #HT #X #HX #Y #HY destruct -IH
lapply (lfxs_fwd_length … HY) -HY #H0
elim (lfxs_inv_zero … HY) -HY *
[ #H1 #H2 destruct -IH /2 width=1 by and3_intro/
| #I #K0 #K2 #V0 #V2 #HK02 #HV02 #H1 #H2 destruct
- elim (IH … HK02) [4,5: /2 width=2 by fqu_fqup, fqu_lref_O/ ]
-
- lapply (lfxs_fwd_length … HY) -HY #H0
- /3 width=1 by fle_lref_length, and3_intro/
- | * #I0 #K0 #V0 #V1 #HLK0 #HV01 #HX
-
- elim (lfxs_inv_lref … HY) -HY // #HV0 #HT0
-
+ elim H2R -H2R #H2R
+ [ <(H2R G0) in HV02; -H2R #HV02
+ elim (IH … HV02 … HK02) /2 width=2 by fqu_fqup, fqu_lref_O/ -IH -HV02 -HK02 #H1V #H2V #H3V
+ | lapply (H2R … HV02) -H2R -HV02 #HV20
+ elim (IH … V0 … HK02) [|*: /2 width=4 by fqu_fqup, fqu_lref_O/ ] -IH -HK02 #H1V #_ #_
+ ]
+ | #f #I #K0 #K2 #Hf #HK02 #H1 #H2 destruct
+ ]
+ | * #I0 #K0 #V0 #V1 #HV01 #HV1X #H destruct
+ elim (lfxs_inv_zero_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct
+ ]
+ | elim (cpx_inv_lref1 … HX) -HX
+ [ #H destruct
+ elim (lfxs_inv_lref … HY) -HY *
+ [ #H0 #H1 destruct /2 width=1 by and3_intro/
+ | #I0 #I2 #K0 #K2 #HK02 #H1 #H2 destruct
+ lapply (lfxs_fwd_length … HK02) #HK
+ elim (IH … HK02) [|*: /2 width=4 by fqu_fqup/ ] -IH -HK02
+ /3 width=5 by and3_intro, fle_lifts_SO/
+ ]
+ | * #I0 #K0 #V1 #HV1 #HV1X #H0 destruct
+ elim (lfxs_inv_lref_bind_sn … HY) -HY #I2 #K2 #HK02 #H destruct
+ lapply (lfxs_fwd_length … HK02) #HK
+ elim (IH … HK02) [|*: /2 width=4 by fqu_fqup/ ] -IH -HV1 -HK02
+ /3 width=5 by fle_lifts_SO, and3_intro/
+ ]
+ ]
| #l #HG #HL #HT #X #HX #Y #HY destruct -IH
lapply (lfxs_fwd_length … HY) -HY #H0
>(cpx_inv_gref1 … HX) -X
]
]
]
-*)
\ No newline at end of file
+*)