- sone refactoring

[helm.git] / matita / matita / lib / lambda-delta / reduction / pr_defs.ma

diff --git a/matita/matita/lib/lambda-delta/reduction/pr_defs.ma b/matita/matita/lib/lambda-delta/reduction/pr_defs.ma
deleted file mode 100644 (file)
index d45cbd0..0000000
--- a/matita/matita/lib/lambda-delta/reduction/pr_defs.ma
+++ /dev/null
@@ -1,81 +0,0 @@
-(*
-    ||M||  This file is part of HELM, an Hypertextual, Electronic
-    ||A||  Library of Mathematics, developed at the Computer Science
-    ||T||  Department of the University of Bologna, Italy.
-    ||I||
-    ||T||
-    ||A||  This file is distributed under the terms of the
-    \   /  GNU General Public License Version 2
-     \ /
-      V_______________________________________________________________ *)
-
-include "lambda-delta/substitution/drop_defs.ma".
-
-(* SINGLE STEP PARALLEL REDUCTION ON TERMS **********************************)
-
-inductive pr: lenv → term → term → Prop ≝
-| pr_sort : ∀L,k. pr L (⋆k) (⋆k)
-| pr_lref : ∀L,i. pr L (#i) (#i)
-| pr_bind : ∀L,I,V1,V2,T1,T2. pr L V1 V2 → pr (L. 𝕓{I} V1) T1 T2 →
-            pr L (𝕓{I} V1. T1) (𝕓{I} V2. T2)
-| pr_flat : ∀L,I,V1,V2,T1,T2. pr L V1 V2 → pr L T1 T2 →
-            pr L (𝕗{I} V1. T1) (𝕗{I} V2. T2)
-| pr_beta : ∀L,V1,V2,W,T1,T2.
-            pr L V1 V2 → pr (L. 𝕓{Abst} W) T1 T2 → (*𝕓*)
-            pr L (𝕚{Appl} V1. 𝕚{Abst} W. T1) (𝕚{Abbr} V2. T2)
-| pr_delta: ∀L,K,V1,V2,V,i.
-            ↑[0,i] K. 𝕓{Abbr} V1 ≡ L → pr K V1 V2 → ↑[0,i+1] V2 ≡ V →
-            pr L (#i) V
-| pr_theta: ∀L,V,V1,V2,W1,W2,T1,T2.
-            pr L V1 V2 → ↑[0,1] V2 ≡ V → pr L W1 W2 → pr (L. 𝕓{Abbr} W1) T1 T2 → (*𝕓*)
-            pr L (𝕚{Appl} V1. 𝕚{Abbr} W1. T1) (𝕚{Abbr} W2. 𝕚{Appl} V. T2)
-| pr_zeta : ∀L,V,T,T1,T2. ↑[0,1] T1 ≡ T → pr L T1 T2 →
-            pr L (𝕚{Abbr} V. T) T2
-| pr_tau  : ∀L,V,T1,T2. pr L T1 T2 → pr L (𝕚{Cast} V. T1) T2
-.
-
-interpretation
-   "single step parallel reduction (term)"
-   'PR L T1 T2 = (pr L T1 T2).
-
-(* Basic properties *********************************************************)
-
-lemma pr_refl: ∀T,L. L ⊢ T ⇒ T.
-#T elim T -T //
-#I elim I -I /2/
-qed.
-
-(* The basic inversion lemmas ***********************************************)
-
-lemma pr_inv_lref2_aux: ∀L,T1,T2. L ⊢ T1 ⇒ T2 → ∀i. T2 = #i →
-                        ∨∨           T1 = #i
-                         | ∃∃K,V1,j. j < i & K ⊢ V1 ⇒ #(i-j-1) &
-                                     ↑[O,j] K. 𝕓{Abbr} V1 ≡ L & T1 = #j
-                         | ∃∃V,T,T0. ↑[O,1] T0 ≡ T & L ⊢ T0 ⇒ #i &
-                                     T1 = 𝕓{Abbr} V. T
-                         | ∃∃V,T.    L ⊢ T ⇒ #i & T1 = 𝕗{Cast} V. T.
-#L #T1 #T2 #H elim H -H L T1 T2
-[ #L #k #i #H destruct
-| #L #j #i /2/
-| #L #I #V1 #V2 #T1 #T2 #_ #_ #_ #_ #i #H destruct
-| #L #I #V1 #V2 #T1 #T2 #_ #_ #_ #_ #i #H destruct
-| #L #V1 #V2 #W #T1 #T2 #_ #_ #_ #_ #i #H destruct
-| #L #K #V1 #V2 #V #j #HLK #HV12 #HV2 #_ #i #H destruct -V;
-  elim (lift_inv_lref2 … HV2) -HV2 * #H1 #H2
-  [ elim (lt_zero_false … H1)
-  | destruct -V2 /3 width=7/
-  ]
-| #L #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #i #H destruct
-| #L #V #T #T1 #T2 #HT1 #HT12 #_ #i #H destruct /3 width=6/
-| #L #V #T1 #T2 #HT12 #_ #i #H destruct /3/
-]
-qed.
-
-lemma pr_inv_lref2: ∀L,T1,i. L ⊢ T1 ⇒ #i →
-                    ∨∨           T1 = #i
-                     | ∃∃K,V1,j. j < i & K ⊢ V1 ⇒ #(i-j-1) &
-                                 ↑[O,j] K. 𝕓{Abbr} V1 ≡ L & T1 = #j
-                     | ∃∃V,T,T0. ↑[O,1] T0 ≡ T & L ⊢ T0 ⇒ #i &
-                                 T1 = 𝕓{Abbr} V. T
-                     | ∃∃V,T.    L ⊢ T ⇒ #i & T1 = 𝕗{Cast} V. T.
-/2/ qed.