(* Basic_2A1: was: cpx_delta *)
lemma cpx_delta_drops (G) (L):
∀I,K,V,V2,W2,i.
- â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9dªG,Kâ\9d« ⊢ V ⬈ V2 →
- â\87§[â\86\91i] V2 â\89\98 W2 â\86\92 â\9dªG,Lâ\9d« ⊢ #i ⬈ W2.
+ â\87©[i] L â\89\98 K.â\93\91[I]V â\86\92 â\9d¨G,Kâ\9d© ⊢ V ⬈ V2 →
+ â\87§[â\86\91i] V2 â\89\98 W2 â\86\92 â\9d¨G,Lâ\9d© ⊢ #i ⬈ W2.
#G #L * #K #V #V2 #W2 #i #HLK *
/3 width=7 by cpg_ell_drops, cpg_delta_drops, ex_intro/
qed.
(* Basic_2A1: was: cpx_inv_atom1 *)
lemma cpx_inv_atom1_drops (G) (L):
- â\88\80I,T2. â\9dªG,Lâ\9d« ⊢ ⓪[I] ⬈ T2 →
+ â\88\80I,T2. â\9d¨G,Lâ\9d© ⊢ ⓪[I] ⬈ T2 →
∨∨ T2 = ⓪[I]
| ∃∃s1,s2. T2 = ⋆s2 & I = Sort s1
- | â\88\83â\88\83J,K,V,V2,i. â\87©[i] L â\89\98 K.â\93\91[J]V & â\9dªG,Kâ\9d« ⊢ V ⬈ V2 & ⇧[↑i] V2 ≘ T2 & I = LRef i.
+ | â\88\83â\88\83J,K,V,V2,i. â\87©[i] L â\89\98 K.â\93\91[J]V & â\9d¨G,Kâ\9d© ⊢ V ⬈ V2 & ⇧[↑i] V2 ≘ T2 & I = LRef i.
#G #L #I #T2 * #c #H elim (cpg_inv_atom1_drops … H) -H *
/4 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex2_2_intro, ex_intro/
qed-.
(* Basic_2A1: was: cpx_inv_lref1 *)
lemma cpx_inv_lref1_drops (G) (L):
- â\88\80T2,i. â\9dªG,Lâ\9d« ⊢ #i ⬈ T2 →
+ â\88\80T2,i. â\9d¨G,Lâ\9d© ⊢ #i ⬈ T2 →
∨∨ T2 = #i
- | â\88\83â\88\83J,K,V,V2. â\87©[i] L â\89\98 K. â\93\91[J]V & â\9dªG,Kâ\9d« ⊢ V ⬈ V2 & ⇧[↑i] V2 ≘ T2.
+ | â\88\83â\88\83J,K,V,V2. â\87©[i] L â\89\98 K. â\93\91[J]V & â\9d¨G,Kâ\9d© ⊢ V ⬈ V2 & ⇧[↑i] V2 ≘ T2.
#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-.