(* Advanced inversion lemmas ************************************************)
-lemma xpr_inv_abst1: â\88\80h,g,a,L,V1,T1,U2. â¦\83h, Lâ¦\84 â\8a¢ â\93\9b{a}V1.T1 â\9e¸[g] U2 →
- â\88\83â\88\83V2,T2. L â\8a¢ V1 â\9e¡ V2 & â¦\83h, L. â\93\9bV1â¦\84 â\8a¢ T1 â\9e¸[g] T2 &
+lemma xpr_inv_abst1: â\88\80h,g,a,L,V1,T1,U2. â¦\83h, Lâ¦\84 â\8a¢ â\93\9b{a}V1.T1 â\80¢â\9e¡[g] U2 →
+ â\88\83â\88\83V2,T2. L â\8a¢ V1 â\9e¡ V2 & â¦\83h, L. â\93\9bV1â¦\84 â\8a¢ T1 â\80¢â\9e¡[g] T2 &
U2 = ⓛ{a}V2. T2.
#h #g #a #L #V1 #T1 #U2 *
[ #H elim (cpr_inv_abst1 … H Abst V1) /3 width=5/
-| * #l #H elim (ssta_inv_bind1 … H) /3 width=5/
+| #l #H elim (ssta_inv_bind1 … H) /3 width=5/
]
qed-.
lemma xpr_lift: ∀L,K,d,e. ⇩[d, e] L ≡ K →
∀T1,U1. ⇧[d, e] T1 ≡ U1 → ∀T2,U2. ⇧[d, e] T2 ≡ U2 →
- â\88\80h,g. â¦\83h, Kâ¦\84 â\8a¢ T1 â\9e¸[g] T2 â\86\92 â¦\83h, Lâ¦\84 â\8a¢ U1 â\9e¸[g] U2.
-#L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #h #g * [2: * ]
+ â\88\80h,g. â¦\83h, Kâ¦\84 â\8a¢ T1 â\80¢â\9e¡[g] T2 â\86\92 â¦\83h, Lâ¦\84 â\8a¢ U1 â\80¢â\9e¡[g] U2.
+#L #K #d #e #HLK #T1 #U1 #HTU1 #T2 #U2 #HTU2 #h #g *
/3 width=9/ /3 width=10/
qed.
lemma xpr_inv_lift1: ∀L,K,d,e. ⇩[d, e] L ≡ K →
- â\88\80T1,U1. â\87§[d, e] T1 â\89¡ U1 â\86\92 â\88\80h,g,U2. â¦\83h, Lâ¦\84 â\8a¢ U1 â\9e¸[g] U2 →
- â\88\83â\88\83T2. â\87§[d, e] T2 â\89¡ U2 & â¦\83h, Kâ¦\84 â\8a¢ T1 â\9e¸[g] T2.
-#L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #U2 * [ #HU12 | * #l #HU12 ]
+ â\88\80T1,U1. â\87§[d, e] T1 â\89¡ U1 â\86\92 â\88\80h,g,U2. â¦\83h, Lâ¦\84 â\8a¢ U1 â\80¢â\9e¡[g] U2 →
+ â\88\83â\88\83T2. â\87§[d, e] T2 â\89¡ U2 & â¦\83h, Kâ¦\84 â\8a¢ T1 â\80¢â\9e¡[g] T2.
+#L #K #d #e #HLK #T1 #U1 #HTU1 #h #g #U2 * [ #HU12 | #l #HU12 ]
[ elim (cpr_inv_lift1 … HLK … HTU1 … HU12) -L -U1 /3 width=3/
| elim (ssta_inv_lift1 … HU12 … HLK … HTU1) -L -U1 /3 width=4/
]