(* Properties with generic slicing for local environments *******************)
(* Note: the main property of simple terms *)
-lemma cpg_inv_appl1_simple: ∀h,r,G,L,V1,T1,U. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡[h, r] U → 𝐒⦃T1⦄ →
- ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h, r] V2 & ⦃G, L⦄ ⊢ T1 ➡[h, r] T2 &
+lemma cpg_inv_appl1_simple: ∀h,c,G,L,V1,T1,U. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡[h, c] U → 𝐒⦃T1⦄ →
+ ∃∃V2,T2. ⦃G, L⦄ ⊢ V1 ➡[h, c] V2 & ⦃G, L⦄ ⊢ T1 ➡[h, c] T2 &
U = ⓐV2.T2.
-#h #r #G #L #V1 #T1 #U #H #HT1
+#h #c #G #L #V1 #T1 #U #H #HT1
elim (cpg_inv_appl1 … H) -H *
[ /2 width=5 by ex3_2_intro/
| #a #V2 #W1 #W2 #U1 #U2 #_ #_ #_ #H #_ destruct