update in groud_2 and models

[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 042e814cdb4b34a4b2718240704da5b3644b9b4f..6411f701ce1ddd4233da43869d4361803beef9c2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma
@@ -98,6 +98,66 @@ lemma cpr_inv_flat1: ∀h,I,G,L,V1,U1,U2. ⦃G, L⦄ ⊢ ⓕ{I}V1.U1 ➡[h] U2 
 ]
 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)
+                   ) → (∀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)
+                   ) → (∀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
+                   ) → (∀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)
+                   ) → (∀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)
+                   ) →
+                   ∀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
+* #c #HC #H generalize in match HC; -HC
+elim H -c -G -L -T1 -T2
+[ /2 width=3 by ex2_intro/
+| #G #L #s #H
+  lapply (isrt_inv_01 … H) -H #H destruct
+| /3 width=4 by ex2_intro/
+| #c #G #L #V1 #V2 #W2 #_ #_ #_ #H
+  elim (isrt_inv_plus_SO_dx … H) -H // #n #_ #H destruct
+| /3 width=4 by ex2_intro/
+| #cV #cT #p #I #G #L #V1 #V2 #T1 #T2 #HV12 #HT12 #IHV #IHT #H
+  elim (isrt_O_inv_max … H) -H #HcV #HcT
+  /4 width=3 by isr_inv_shift, ex2_intro/
+| #cV #cT #G #L #V1 #V2 #T1 #T2 #HV12 #HT12 #IHV #IHT #H
+  elim (isrt_O_inv_max … H) -H #HcV #HcT
+  /4 width=3 by isr_inv_shift, ex2_intro/
+| #cU #cT #G #L #U1 #U2 #T1 #T2 #HUT #HU12 #HT12 #IHU #IHT #H
+  elim (isrt_O_inv_max … H) -H #HcV #HcT
+  /3 width=3 by ex2_intro/
+| /4 width=4 by isrt_inv_plus_O_dx, ex2_intro/
+| /4 width=4 by isrt_inv_plus_O_dx, ex2_intro/
+| #c #G #L #U1 #U2 #T #_ #_ #H
+  elim (isrt_inv_plus_SO_dx … H) -H // #n #_ #H destruct
+| #cV #cW #cT #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #HT12 #IHV #IHW #IHT #H
+  lapply (isrt_inv_plus_O_dx … H ?) -H // #H
+  elim (isrt_O_inv_max … H) -H #H #HcT
+  elim (isrt_O_inv_max … H) -H #HcV #HcW
+  /4 width=3 by isr_inv_shift, ex2_intro/
+| #cV #cW #cT #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HW12 #HT12 #IHV #IHW #IHT #H
+  lapply (isrt_inv_plus_O_dx … H ?) -H // #H
+  elim (isrt_O_inv_max … H) -H #H #HcT
+  elim (isrt_O_inv_max … H) -H #HcV #HcW
+  /4 width=4 by isr_inv_shift, ex2_intro/
+]
+qed-.
+
 (* Basic_1: removed theorems 12:
             pr0_subst0_back pr0_subst0_fwd pr0_subst0
             pr0_delta1