more lemmas to prove and a correction in subst

[helm.git] / matita / matita / lib / lambda-delta / substitution / subst.ma

diff --git a/matita/matita/lib/lambda-delta/substitution/subst.ma b/matita/matita/lib/lambda-delta/substitution/subst.ma
index e09b37f35b93246f177e27d8d47d9af4d947f2ad..18eb6c5269e0f52be05dd2eee640b4e3998b5c08 100644 (file)
--- a/matita/matita/lib/lambda-delta/substitution/subst.ma
+++ b/matita/matita/lib/lambda-delta/substitution/subst.ma
@@ -9,27 +9,31 @@
      \ /
       V_______________________________________________________________ *)
 
-include "lambda-delta/language/lenv.ma".
+include "lambda-delta/syntax/lenv.ma".
 include "lambda-delta/substitution/lift.ma".
 
 (* TELESCOPIC SUBSTITUTION **************************************************)
 
 inductive subst: lenv → term → nat → nat → term → Prop ≝
-   | subst_sort   : ∀L,k,d,e. subst L (⋆k) d e (⋆k)
-   | subst_lref_lt: ∀L,i,d,e. i < d → subst L (#i) d e (#i)
-   | subst_lref_O : ∀L,V,e. 0 < e → subst (L. ♭Abbr V) #0 0 e V
-   | subst_lref_S : ∀L,I,V,i,T1,T2,d,e. 
-                    d ≤ i → i < d + e → subst L #i d e T1 → [d,1]↑ T1 ≡ T2 →
-                    subst (L. ♭I V) #(i + 1) (d + 1) e T2
-   | subst_lref_ge: ∀L,i,d,e. d + e ≤ i → subst L (#i) d e (#(i - e))
-   | subst_con2   : ∀L,I,V1,V2,T1,T2,d,e.
-                    subst L V1 d e V2 → subst (L. ♭I V1) T1 (d + 1) e T2 →
-                    subst L (♭I V1. T1) d e (♭I V2. T2)
+| subst_sort   : ∀L,k,d,e. subst L (⋆k) d e (⋆k)
+| subst_lref_lt: ∀L,i,d,e. i < d → subst L (#i) d e (#i)
+| subst_lref_O : ∀L,V1,V2,e. subst L V1 0 e V2 →
+                 subst (L. 𝕓{Abbr} V1) #0 0 (e + 1) V2
+| subst_lref_S : ∀L,I,V,i,T1,T2,d,e.
+                 d ≤ i → i < d + e → subst L #i d e T1 → ↑[d,1] T1 ≡ T2 →
+                 subst (L. 𝕓{I} V) #(i + 1) (d + 1) e T2
+| subst_lref_ge: ∀L,i,d,e. d + e ≤ i → subst L (#i) d e (#(i - e))
+| subst_bind   : ∀L,I,V1,V2,T1,T2,d,e.
+                 subst L V1 d e V2 → subst (L. 𝕓{I} V1) T1 (d + 1) e T2 →
+                 subst L (𝕓{I} V1. T1) d e (𝕓{I} V2. T2)
+| subst_flat   : ∀L,I,V1,V2,T1,T2,d,e.
+                 subst L V1 d e V2 → subst L T1 d e T2 →
+                 subst L (𝕗{I} V1. T1) d e (𝕗{I} V2. T2)
 .
 
 interpretation "telescopic substritution" 'RSubst L T1 d e T2 = (subst L T1 d e T2).
 
-lemma subst_lift_inv: ∀d,e,T1,T2. [d,e]↑ T1 ≡ T2 → ∀L. [d,e]← L / T2 ≡ T1.
+lemma subst_lift_inv: ∀d,e,T1,T2. ↑[d,e] T1 ≡ T2 → ∀L. L ⊢ ↓[d,e] T2 ≡ T1.
 #d #e #T1 #T2 #H elim H -H d e T1 T2 /2/
 #i #d #e #Hdi #L >(minus_plus_m_m i e) in ⊢ (? ? ? ? ? %) /3/ (**) (* use \ldots *)
 qed.