(* Advanced properties ******************************************************)
-lemma cpxs_delta: â\88\80h,I,G,K,V1,V2. â¦\83G,Kâ¦\84 ⊢ V1 ⬈*[h] V2 →
- ∀W2. ⇧*[1] V2 ≘ W2 → ⦃G,K.ⓑ{I}V1⦄ ⊢ #0 ⬈*[h] W2.
+lemma cpxs_delta: â\88\80h,I,G,K,V1,V2. â\9dªG,Kâ\9d« ⊢ V1 ⬈*[h] V2 →
+ ∀W2. ⇧[1] V2 ≘ W2 → ❪G,K.ⓑ[I]V1❫ ⊢ #0 ⬈*[h] W2.
#h #I #G #K #V1 #V2 #H @(cpxs_ind … H) -V2
[ /3 width=3 by cpx_cpxs, cpx_delta/
| #V #V2 #_ #HV2 #IH #W2 #HVW2
- elim (lifts_total V (ð\9d\90\94â\9d´1â\9dµ))
+ elim (lifts_total V (ð\9d\90\94â\9d¨1â\9d©))
/5 width=11 by cpxs_strap1, cpx_lifts_bi, drops_refl, drops_drop/
]
qed.
-lemma cpxs_lref: â\88\80h,I,G,K,T,i. â¦\83G,Kâ¦\84 ⊢ #i ⬈*[h] T →
- ∀U. ⇧*[1] T ≘ U → ⦃G,K.ⓘ{I}⦄ ⊢ #↑i ⬈*[h] U.
+lemma cpxs_lref: â\88\80h,I,G,K,T,i. â\9dªG,Kâ\9d« ⊢ #i ⬈*[h] T →
+ ∀U. ⇧[1] T ≘ U → ❪G,K.ⓘ[I]❫ ⊢ #↑i ⬈*[h] U.
#h #I #G #K #T #i #H @(cpxs_ind … H) -T
[ /3 width=3 by cpx_cpxs, cpx_lref/
| #T0 #T #_ #HT2 #IH #U #HTU
- elim (lifts_total T0 (ð\9d\90\94â\9d´1â\9dµ))
+ elim (lifts_total T0 (ð\9d\90\94â\9d¨1â\9d©))
/5 width=11 by cpxs_strap1, cpx_lifts_bi, drops_refl, drops_drop/
]
qed.
(* Basic_2A1: was: cpxs_delta *)
lemma cpxs_delta_drops: ∀h,I,G,L,K,V1,V2,i.
- ⇩*[i] L ≘ K.ⓑ{I}V1 → ⦃G,K⦄ ⊢ V1 ⬈*[h] V2 →
- ∀W2. ⇧*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ⬈*[h] W2.
+ ⇩[i] L ≘ K.ⓑ[I]V1 → ❪G,K❫ ⊢ V1 ⬈*[h] V2 →
+ ∀W2. ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈*[h] W2.
#h #I #G #L #K #V1 #V2 #i #HLK #H @(cpxs_ind … H) -V2
[ /3 width=7 by cpx_cpxs, cpx_delta_drops/
| #V #V2 #_ #HV2 #IH #W2 #HVW2
- elim (lifts_total V (ð\9d\90\94â\9d´â\86\91iâ\9dµ))
+ elim (lifts_total V (ð\9d\90\94â\9d¨â\86\91iâ\9d©))
/4 width=11 by cpxs_strap1, cpx_lifts_bi, drops_isuni_fwd_drop2/
]
qed.
(* Advanced inversion lemmas ************************************************)
-lemma cpxs_inv_zero1: â\88\80h,G,L,T2. â¦\83G,Lâ¦\84 ⊢ #0 ⬈*[h] T2 →
+lemma cpxs_inv_zero1: â\88\80h,G,L,T2. â\9dªG,Lâ\9d« ⊢ #0 ⬈*[h] T2 →
T2 = #0 ∨
- â\88\83â\88\83I,K,V1,V2. â¦\83G,Kâ¦\84 â\8a¢ V1 â¬\88*[h] V2 & â\87§*[1] V2 ≘ T2 &
- L = K.ⓑ{I}V1.
+ â\88\83â\88\83I,K,V1,V2. â\9dªG,Kâ\9d« â\8a¢ V1 â¬\88*[h] V2 & â\87§[1] V2 ≘ T2 &
+ L = K.ⓑ[I]V1.
#h #G #L #T2 #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
#T #T2 #_ #HT2 *
[ #H destruct
]
qed-.
-lemma cpxs_inv_lref1: â\88\80h,G,L,T2,i. â¦\83G,Lâ¦\84 ⊢ #↑i ⬈*[h] T2 →
+lemma cpxs_inv_lref1: â\88\80h,G,L,T2,i. â\9dªG,Lâ\9d« ⊢ #↑i ⬈*[h] T2 →
T2 = #(↑i) ∨
- â\88\83â\88\83I,K,T. â¦\83G,Kâ¦\84 â\8a¢ #i â¬\88*[h] T & â\87§*[1] T â\89\98 T2 & L = K.â\93\98{I}.
+ â\88\83â\88\83I,K,T. â\9dªG,Kâ\9d« â\8a¢ #i â¬\88*[h] T & â\87§[1] T â\89\98 T2 & L = K.â\93\98[I].
#h #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
#T #T2 #_ #HT2 *
[ #H destruct
qed-.
(* Basic_2A1: was: cpxs_inv_lref1 *)
-lemma cpxs_inv_lref1_drops: â\88\80h,G,L,T2,i. â¦\83G,Lâ¦\84 ⊢ #i ⬈*[h] T2 →
+lemma cpxs_inv_lref1_drops: â\88\80h,G,L,T2,i. â\9dªG,Lâ\9d« ⊢ #i ⬈*[h] T2 →
T2 = #i ∨
- ∃∃I,K,V1,T1. ⇩*[i] L ≘ K.ⓑ{I}V1 & ⦃G,K⦄ ⊢ V1 ⬈*[h] T1 &
- ⇧*[↑i] T1 ≘ T2.
+ ∃∃I,K,V1,T1. ⇩[i] L ≘ K.ⓑ[I]V1 & ❪G,K❫ ⊢ V1 ⬈*[h] T1 &
+ ⇧[↑i] T1 ≘ T2.
#h #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
#T #T2 #_ #HT2 *
[ #H destruct