X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Fcpm_drops.ma;h=bc9463c958390c5a16ec878d6d4b3f5bf6d30fcf;hb=647b419e96770d90a82d7a9e5e8843566a9f93ee;hp=46a1e039d1405f482d6a54f22f777dbbc5968684;hpb=e0f7a5025addf275e40372da3a39b0adacc8106f;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
index 46a1e039d..bc9463c95 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
@@ -50,27 +50,27 @@ qed-.
 (* Basic_1: includes: pr2_delta1 *)
 (* Basic_2A1: includes: cpr_delta *)
 lemma cpm_delta_drops: ∀n,h,G,L,K,V,V2,W2,i.
-                       ⬇*[i] L ≘ K.ⓓV → ⦃G, K⦄ ⊢ V ➡[n, h] V2 →
-                       ⬆*[↑i] V2 ≘ W2 → ⦃G, L⦄ ⊢ #i ➡[n, h] W2.
+                       ⬇*[i] L ≘ K.ⓓV → ⦃G,K⦄ ⊢ V ➡[n,h] V2 →
+                       ⬆*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ➡[n,h] W2.
 #n #h #G #L #K #V #V2 #W2 #i #HLK *
 /3 width=8 by cpg_delta_drops, ex2_intro/
 qed.
 
 lemma cpm_ell_drops: ∀n,h,G,L,K,V,V2,W2,i.
-                     ⬇*[i] L ≘ K.ⓛV → ⦃G, K⦄ ⊢ V ➡[n, h] V2 →
-                     ⬆*[↑i] V2 ≘ W2 → ⦃G, L⦄ ⊢ #i ➡[↑n, h] W2.
+                     ⬇*[i] L ≘ K.ⓛV → ⦃G,K⦄ ⊢ V ➡[n,h] V2 →
+                     ⬆*[↑i] V2 ≘ W2 → ⦃G,L⦄ ⊢ #i ➡[↑n,h] W2.
 #n #h #G #L #K #V #V2 #W2 #i #HLK *
 /3 width=8 by cpg_ell_drops, isrt_succ, ex2_intro/
 qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpm_inv_atom1_drops: ∀n,h,I,G,L,T2. ⦃G, L⦄ ⊢ ⓪{I} ➡[n, h] T2 →
+lemma cpm_inv_atom1_drops: ∀n,h,I,G,L,T2. ⦃G,L⦄ ⊢ ⓪{I} ➡[n,h] T2 →
                            ∨∨ T2 = ⓪{I} ∧ n = 0
-                            | ∃∃s. T2 = ⋆(next h s) & I = Sort s & n = 1
-                            | ∃∃K,V,V2,i. ⬇*[i] L ≘ K.ⓓV & ⦃G, K⦄ ⊢ V ➡[n, h] V2 &
+                            | ∃∃s. T2 = ⋆(⫯[h]s) & I = Sort s & n = 1
+                            | ∃∃K,V,V2,i. ⬇*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V ➡[n,h] V2 &
                                           ⬆*[↑i] V2 ≘ T2 & I = LRef i
-                            | ∃∃m,K,V,V2,i. ⬇*[i] L ≘ K.ⓛV & ⦃G, K⦄ ⊢ V ➡[m, h] V2 &
+                            | ∃∃m,K,V,V2,i. ⬇*[i] L ≘ K.ⓛV & ⦃G,K⦄ ⊢ V ➡[m,h] V2 &
                                             ⬆*[↑i] V2 ≘ T2 & I = LRef i & n = ↑m.
 #n #h #I #G #L #T2 * #c #Hc #H elim (cpg_inv_atom1_drops … H) -H *
 [ #H1 #H2 destruct lapply (isrt_inv_00 … Hc) -Hc
@@ -85,11 +85,11 @@ lemma cpm_inv_atom1_drops: ∀n,h,I,G,L,T2. ⦃G, L⦄ ⊢ ⓪{I} ➡[n, h] T2 
 ]
 qed-.
 
-lemma cpm_inv_lref1_drops: ∀n,h,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[n, h] T2 →
+lemma cpm_inv_lref1_drops: ∀n,h,G,L,T2,i. ⦃G,L⦄ ⊢ #i ➡[n,h] T2 →
                            ∨∨ T2 = #i ∧ n = 0
-                            | ∃∃K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G, K⦄ ⊢ V ➡[n, h] V2 &
+                            | ∃∃K,V,V2. ⬇*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V ➡[n,h] V2 &
                                         ⬆*[↑i] V2 ≘ T2
-                            | ∃∃m,K,V,V2. ⬇*[i] L ≘ K. ⓛV & ⦃G, K⦄ ⊢ V ➡[m, h] V2 &
+                            | ∃∃m,K,V,V2. ⬇*[i] L ≘ K. ⓛV & ⦃G,K⦄ ⊢ V ➡[m,h] V2 &
                                           ⬆*[↑i] V2 ≘ T2 & n = ↑m.
 #n #h #G #L #T2 #i * #c #Hc #H elim (cpg_inv_lref1_drops … H) -H *
 [ #H1 #H2 destruct lapply (isrt_inv_00 … Hc) -Hc
@@ -104,9 +104,9 @@ qed-.
 
 (* Advanced forward lemmas **************************************************)
 
-fact cpm_fwd_plus_aux (n) (h): ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 →
+fact cpm_fwd_plus_aux (n) (h): ∀G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 →
                                ∀n1,n2. n1+n2 = n →
-                               ∃∃T. ⦃G, L⦄ ⊢ T1 ➡[n1, h] T & ⦃G, L⦄ ⊢ T ➡[n2, h] T2.
+                               ∃∃T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T & ⦃G,L⦄ ⊢ T ➡[n2,h] T2.
 #n #h #G #L #T1 #T2 #H @(cpm_ind … H) -G -L -T1 -T2 -n
 [ #I #G #L #n1 #n2 #H
   elim (plus_inv_O3 … H) -H #H1 #H2 destruct
@@ -143,9 +143,9 @@ fact cpm_fwd_plus_aux (n) (h): ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 →
   elim IHU [|*: // ] -IHU #U #HU1 #HU2
   elim IHT [|*: // ] -IHT #T #HT1 #HT2
   /3 width=5 by cpm_cast, ex2_intro/
-| #n #G #K #V #T1 #T2 #V2 #_ #IH #HVT2 #n1 #n2 #H destruct
+| #n #G #K #V #U1 #T1 #T2 #HTU1 #_ #IH #n1 #n2 #H destruct
   elim IH [|*: // ] -IH #T #HT1 #HT2
-  /3 width=6 by cpm_zeta, cpm_bind, ex2_intro/
+  /3 width=3 by cpm_zeta, ex2_intro/
 | #n #G #L #U #T1 #T2 #_ #IH #n1 #n2 #H destruct
   elim IH [|*: // ] -IH #T #HT1 #HT2
   /3 width=3 by cpm_eps, ex2_intro/
@@ -165,6 +165,6 @@ fact cpm_fwd_plus_aux (n) (h): ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 →
 ]
 qed-.
 
-lemma cpm_fwd_plus (h) (G) (L): ∀n1,n2,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n1+n2, h] T2 →
-                                ∃∃T. ⦃G, L⦄ ⊢ T1 ➡[n1, h] T & ⦃G, L⦄ ⊢ T ➡[n2, h] T2.
+lemma cpm_fwd_plus (h) (G) (L): ∀n1,n2,T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n1+n2,h] T2 →
+                                ∃∃T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T & ⦃G,L⦄ ⊢ T ➡[n2,h] T2.
 /2 width=3 by cpm_fwd_plus_aux/ qed-.