(* Basic_2A1: was: cpx_delta *)
lemma cpx_delta_drops: ∀h,I,G,L,K,V,V2,W2,i.
- ⇩*[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⬈[h] V2 →
- ⇧*[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈[h] W2.
+ ⇩[i] L ≘ K.ⓑ[I]V → ❪G,K❫ ⊢ V ⬈[h] V2 →
+ ⇧[↑i] V2 ≘ W2 → ❪G,L❫ ⊢ #i ⬈[h] W2.
#h * #G #L #K #V #V2 #W2 #i #HLK *
/3 width=7 by cpg_ell_drops, cpg_delta_drops, ex_intro/
qed.
lemma cpx_inv_atom1_drops: ∀h,I,G,L,T2. ❪G,L❫ ⊢ ⓪[I] ⬈[h] T2 →
∨∨ T2 = ⓪[I]
| ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s
- | ∃∃J,K,V,V2,i. ⇩*[i] L ≘ K.ⓑ[J]V & ❪G,K❫ ⊢ V ⬈[h] V2 &
- ⇧*[↑i] V2 ≘ T2 & I = LRef i.
+ | ∃∃J,K,V,V2,i. ⇩[i] L ≘ K.ⓑ[J]V & ❪G,K❫ ⊢ V ⬈[h] V2 &
+ ⇧[↑i] V2 ≘ T2 & I = LRef i.
#h #I #G #L #T2 * #c #H elim (cpg_inv_atom1_drops … H) -H *
/4 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex2_intro, ex_intro/
qed-.
(* Basic_2A1: was: cpx_inv_lref1 *)
lemma cpx_inv_lref1_drops: ∀h,G,L,T2,i. ❪G,L❫ ⊢ #i ⬈[h] T2 →
T2 = #i ∨
- ∃∃J,K,V,V2. ⇩*[i] L ≘ K. ⓑ[J]V & ❪G,K❫ ⊢ V ⬈[h] V2 &
- ⇧*[↑i] V2 ≘ T2.
+ ∃∃J,K,V,V2. ⇩[i] L ≘ K. ⓑ[J]V & ❪G,K❫ ⊢ V ⬈[h] V2 &
+ ⇧[↑i] V2 ≘ T2.
#h #G #L #T1 #i * #c #H elim (cpg_inv_lref1_drops … H) -H *
/4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/
qed-.