-lemma cpm_inv_atom1_drops: ∀h,n,I,G,L,T2. ❪G,L❫ ⊢ ⓪[I] ➡[h,n] T2 →
- ∨∨ T2 = ⓪[I] ∧ n = 0
- | ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s & n = 1
- | ∃∃K,V,V2,i. ⇩[i] L ≘ K.ⓓV & ❪G,K❫ ⊢ V ➡[h,n] V2 &
- ⇧[↑i] V2 ≘ T2 & I = LRef i
- | ∃∃m,K,V,V2,i. ⇩[i] L ≘ K.ⓛV & ❪G,K❫ ⊢ V ➡[h,m] V2 &
- ⇧[↑i] V2 ≘ T2 & I = LRef i & n = ↑m.
-#h #n #I #G #L #T2 * #c #Hc #H elim (cpg_inv_atom1_drops … H) -H *
+lemma cpm_inv_atom1_drops (h) (n) (G) (L):
+ ∀I,T2. ❪G,L❫ ⊢ ⓪[I] ➡[h,n] T2 →
+ ∨∨ ∧∧ T2 = ⓪[I] & n = 0
+ | ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s & n = 1
+ | ∃∃K,V,V2,i. ⇩[i] L ≘ K.ⓓV & ❪G,K❫ ⊢ V ➡[h,n] V2 & ⇧[↑i] V2 ≘ T2 & I = LRef i
+ | ∃∃m,K,V,V2,i. ⇩[i] L ≘ K.ⓛV & ❪G,K❫ ⊢ V ➡[h,m] V2 & ⇧[↑i] V2 ≘ T2 & I = LRef i & n = ↑m.
+#h #n #G #L #I #T2 * #c #Hc #H elim (cpg_inv_atom1_drops … H) -H *