renaming

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma
index 5751df0c9a8f7bfe4066314da13faa70241df12f..091282ef316e06447346846c3f54e05b9a14f480 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma
@@ -101,29 +101,29 @@ qed-.
 
 (* Basic eliminators ********************************************************)
 
-lemma cpr_ind (h): ∀R:relation4 genv lenv term term.
-                   (∀I,G,L. R G L (⓪{I}) (⓪{I})) →
-                   (∀G,K,V1,V2,W2. ⦃G, K⦄ ⊢ V1 ➡[h] V2 → R G K V1 V2 →
-                     ⬆*[1] V2 ≘ W2 → R G (K.ⓓV1) (#0) W2
-                   ) → (∀I,G,K,T,U,i. ⦃G, K⦄ ⊢ #i ➡[h] T → R G K (#i) T →
-                     ⬆*[1] T ≘ U → R G (K.ⓘ{I}) (#↑i) (U)
+lemma cpr_ind (h): ∀Q:relation4 genv lenv term term.
+                   (∀I,G,L. Q G L (⓪{I}) (⓪{I})) →
+                   (∀G,K,V1,V2,W2. ⦃G, K⦄ ⊢ V1 ➡[h] V2 → Q G K V1 V2 →
+                     ⬆*[1] V2 ≘ W2 → Q G (K.ⓓV1) (#0) W2
+                   ) → (∀I,G,K,T,U,i. ⦃G, K⦄ ⊢ #i ➡[h] T → Q G K (#i) T →
+                     ⬆*[1] T ≘ U → Q G (K.ⓘ{I}) (#↑i) (U)
                    ) → (∀p,I,G,L,V1,V2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L.ⓑ{I}V1⦄ ⊢ T1 ➡[h] T2 →
-                     R G L V1 V2 → R G (L.ⓑ{I}V1) T1 T2 → R G L (ⓑ{p,I}V1.T1) (ⓑ{p,I}V2.T2)
+                     Q G L V1 V2 → Q G (L.ⓑ{I}V1) T1 T2 → Q G L (ⓑ{p,I}V1.T1) (ⓑ{p,I}V2.T2)
                    ) → (∀I,G,L,V1,V2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L⦄ ⊢ T1 ➡[h] T2 →
-                     R G L V1 V2 → R G L T1 T2 → R G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
-                   ) → (∀G,L,V,T1,T,T2. ⦃G, L.ⓓV⦄ ⊢ T1 ➡[h] T → R G (L.ⓓV) T1 T →
-                     ⬆*[1] T2 ≘ T → R G L (+ⓓV.T1) T2
-                   ) → (∀G,L,V,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 → R G L T1 T2 →
-                     R G L (ⓝV.T1) T2
+                     Q G L V1 V2 → Q G L T1 T2 → Q G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
+                   ) → (∀G,L,V,T1,T,T2. ⦃G, L.ⓓV⦄ ⊢ T1 ➡[h] T → Q G (L.ⓓV) T1 T →
+                     ⬆*[1] T2 ≘ T → Q G L (+ⓓV.T1) T2
+                   ) → (∀G,L,V,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 → Q G L T1 T2 →
+                     Q G L (ⓝV.T1) T2
                    ) → (∀p,G,L,V1,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V2 → ⦃G, L⦄ ⊢ W1 ➡[h] W2 → ⦃G, L.ⓛW1⦄ ⊢ T1 ➡[h] T2 →
-                     R G L V1 V2 → R G L W1 W2 → R G (L.ⓛW1) T1 T2 →
-                     R G L (ⓐV1.ⓛ{p}W1.T1) (ⓓ{p}ⓝW2.V2.T2)
+                     Q G L V1 V2 → Q G L W1 W2 → Q G (L.ⓛW1) T1 T2 →
+                     Q G L (ⓐV1.ⓛ{p}W1.T1) (ⓓ{p}ⓝW2.V2.T2)
                    ) → (∀p,G,L,V1,V,V2,W1,W2,T1,T2. ⦃G, L⦄ ⊢ V1 ➡[h] V → ⦃G, L⦄ ⊢ W1 ➡[h] W2 → ⦃G, L.ⓓW1⦄ ⊢ T1 ➡[h] T2 →
-                     R G L V1 V → R G L W1 W2 → R G (L.ⓓW1) T1 T2 →
-                     ⬆*[1] V ≘ V2 → R G L (ⓐV1.ⓓ{p}W1.T1) (ⓓ{p}W2.ⓐV2.T2)
+                     Q G L V1 V → Q G L W1 W2 → Q G (L.ⓓW1) T1 T2 →
+                     ⬆*[1] V ≘ V2 → Q G L (ⓐV1.ⓓ{p}W1.T1) (ⓓ{p}W2.ⓐV2.T2)
                    ) →
-                   ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 → R G L T1 T2.
-#h #R #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #IH8 #IH9 #G #L #T1 #T2
+                   ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h] T2 → Q G L T1 T2.
+#h #Q #IH1 #IH2 #IH3 #IH4 #IH5 #IH6 #IH7 #IH8 #IH9 #G #L #T1 #T2
 @(insert_eq_0 … 0) #n #H
 @(cpm_ind … H) -G -L -T1 -T2 -n /3 width=4 by/
 [ #G #L #s #H destruct