- the shift function is now defined and cpr_shift_fwd is proved

[helm.git] / matita / matita / contribs / lambda-delta / Basic-2 / reduction / cpr.ma

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr.ma b/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr.ma
index 21169192cb74c759affea24e2dddcd59e6ed79e6..e06b8fa6d49b7f3c987d3548956b4ac795b914f5 100644 (file)
--- a/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "Basic-2/grammar/cl_shift.ma".
 include "Basic-2/reduction/tpr.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
@@ -29,22 +30,32 @@ lemma cpr_pr: ∀T1,T2. T1 ⇒ T2 → ∀L. L ⊢ T1 ⇒ T2.
 /2/ qed.
 
 lemma cpr_tps: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ≫ T2 → L ⊢ T1 ⇒ T2.
-/3 width=5/ qed. 
+/3 width=5/ qed.
 
 lemma cpr_refl: ∀L,T. L ⊢ T ⇒ T.
 /2/ qed.
 
+lemma cpr_bind_sn: ∀I,L,V1,V2,T1,T2. L ⊢ V1 ⇒ V2 → T1 ⇒ T2 →
+                   L ⊢ 𝕓{I} V1. T1 ⇒ 𝕓{I} V2. T2.
+#I #L #V1 #V2 #T1 #T2 * /3 width=5/
+qed.
+
+lemma cpr_bind_dx: ∀I,L,V1,V2,T1,T2. V1 ⇒ V2 → L. 𝕓{I} V2 ⊢ T1 ⇒ T2 →
+                   L ⊢ 𝕓{I} V1. T1 ⇒ 𝕓{I} V2. T2.
+#I #L #V1 #V2 #T1 #T2 #HV12 * #T #HT1 normalize #HT2
+elim (tps_split_up … HT2 1 ? ?) -HT2 // #T0 <minus_n_O #HT0 normalize <minus_plus_m_m #HT02
+lapply (tps_leq_repl … HT0 (⋆. 𝕓{I} V2) ?) -HT0 /2/ #HT0 /3 width=5/
+qed.
+
 (* NOTE: new property *)
 lemma cpr_flat: ∀I,L,V1,V2,T1,T2.
                 L ⊢ V1 ⇒ V2 → L ⊢ T1 ⇒ T2 → L ⊢ 𝕗{I} V1. T1 ⇒ 𝕗{I} V2. T2.
 #I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 * /3 width=5/
 qed.
 
-lemma cpr_delta: ∀L,K,V1,V2,V,i.
-                 ↓[0, i] L ≡ K. 𝕓{Abbr} V1 → K ⊢ V1 [0, |L| - i - 1] ≫ V2 →
-                 ↑[0, i + 1] V2 ≡ V → L ⊢ #i ⇒ V.
-#L #K #V1 #V2 #V #i #HLK #HV12 #HV2
-@ex2_1_intro [2: // | skip ] /3 width=8/ (**) (* /4/ is too slow *)
+lemma cpr_delta: ∀L,K,V,W,i.
+                 ↓[0, i] L ≡ K. 𝕓{Abbr} V → ↑[0, i + 1] V ≡ W → L ⊢ #i ⇒ W.
+/3/
 qed.
 
 lemma cpr_cast: ∀L,V,T1,T2.
@@ -53,3 +64,17 @@ lemma cpr_cast: ∀L,V,T1,T2.
 qed.
 
 (* Basic inversion lemmas ***************************************************)
+
+lemma cpr_inv_lsort: ∀T1,T2. ⋆ ⊢ T1 ⇒ T2 → T1 ⇒ T2.
+#T1 #T2 * #T #HT normalize #HT2
+<(tps_inv_refl0 … HT2) -HT2 //
+qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma cpr_shift_fwd: ∀L,T1,T2. L ⊢ T1 ⇒ T2 → L @ T1 ⇒ L @ T2.
+#L elim L -L
+[ /2/
+| normalize /3/
+].
+qed.