-lemma cpx_inv_atom1_drops: ∀h,I,G,L,T2. ⦃G, L⦄ ⊢ ⓪{I} ⬈[h] T2 →
- ∨∨ T2 = ⓪{I}
- | ∃∃s. T2 = ⋆(next 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.
-#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/
+lemma cpx_inv_atom1_drops (G) (L):
+ ∀I,T2. ❨G,L❩ ⊢ ⓪[I] ⬈ T2 →
+ ∨∨ T2 = ⓪[I]
+ | ∃∃s1,s2. T2 = ⋆s2 & I = Sort s1
+ | ∃∃J,K,V,V2,i. ⇩[i] L ≘ K.ⓑ[J]V & ❨G,K❩ ⊢ 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/