update in basic_2

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

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 790970db3cb5cec03c3e9debc49fb24f4219eda7..f5915aeff374624155cde601ade882c918166759 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm_drops.ma
@@ -22,15 +22,15 @@ include "basic_2/rt_transition/cpm.ma".
 (* Basic_1: includes: pr2_delta1 *)
 (* Basic_2A1: includes: cpr_delta *)
 lemma cpm_delta_drops: ∀n,h,G,L,K,V,V2,W2,i.
-                       â¬\87*[i] L â\89¡ K.ⓓV → ⦃G, K⦄ ⊢ V ➡[n, h] V2 →
-                       â¬\86*[⫯i] V2 â\89¡ W2 → ⦃G, L⦄ ⊢ #i ➡[n, h] W2.
+                       â¬\87*[i] L â\89\98 K.ⓓV → ⦃G, K⦄ ⊢ V ➡[n, h] V2 →
+                       â¬\86*[â\86\91i] V2 â\89\98 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.
-                     â¬\87*[i] L â\89¡ K.ⓛV → ⦃G, K⦄ ⊢ V ➡[n, h] V2 →
-                     â¬\86*[⫯i] V2 â\89¡ W2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡[⫯n, h] W2.
+                     â¬\87*[i] L â\89\98 K.ⓛV → ⦃G, K⦄ ⊢ V ➡[n, h] V2 →
+                     â¬\86*[â\86\91i] V2 â\89\98 W2 â\86\92 â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡[â\86\91n, h] W2.
 #n #h #G #L #K #V #V2 #W2 #i #HLK *
 /3 width=8 by cpg_ell_drops, isrt_succ, ex2_intro/
 qed.
@@ -40,10 +40,10 @@ qed.
 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
-                            | â\88\83â\88\83K,V,V2,i. â¬\87*[i] L â\89¡ K.ⓓV & ⦃G, K⦄ ⊢ V ➡[n, h] V2 &
-                                          â¬\86*[⫯i] V2 â\89¡ T2 & I = LRef i
-                            | ∃∃k,K,V,V2,i. ⬇*[i] L ≡ K.ⓛV & ⦃G, K⦄ ⊢ V ➡[k, h] V2 &
-                                            â¬\86*[⫯i] V2 â\89¡ T2 & I = LRef i & n = ⫯k.
+                            | â\88\83â\88\83K,V,V2,i. â¬\87*[i] L â\89\98 K.ⓓV & ⦃G, K⦄ ⊢ V ➡[n, h] V2 &
+                                          â¬\86*[â\86\91i] V2 â\89\98 T2 & I = LRef i
+                            | ∃∃m,K,V,V2,i. ⬇*[i] L ≘ K.ⓛV & ⦃G, K⦄ ⊢ V ➡[m, h] V2 &
+                                            â¬\86*[â\86\91i] V2 â\89\98 T2 & I = LRef i & n = â\86\91m.
 #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
   /3 width=1 by or4_intro0, conj/
@@ -59,10 +59,10 @@ qed-.
 
 lemma cpm_inv_lref1_drops: ∀n,h,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[n, h] T2 →
                            ∨∨ T2 = #i ∧ n = 0
-                            | â\88\83â\88\83K,V,V2. â¬\87*[i] L â\89¡ K. ⓓV & ⦃G, K⦄ ⊢ V ➡[n, h] V2 &
-                                        â¬\86*[⫯i] V2 â\89¡ T2
-                            | ∃∃k,K,V,V2. ⬇*[i] L ≡ K. ⓛV & ⦃G, K⦄ ⊢ V ➡[k, h] V2 &
-                                          â¬\86*[⫯i] V2 â\89¡ T2 & n = ⫯k.
+                            | â\88\83â\88\83K,V,V2. â¬\87*[i] L â\89\98 K.ⓓV & ⦃G, K⦄ ⊢ V ➡[n, h] V2 &
+                                        â¬\86*[â\86\91i] V2 â\89\98 T2
+                            | ∃∃m,K,V,V2. ⬇*[i] L ≘ K. ⓛV & ⦃G, K⦄ ⊢ V ➡[m, h] V2 &
+                                          â¬\86*[â\86\91i] V2 â\89\98 T2 & n = â\86\91m.
 #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
   /3 width=1 by or3_intro0, conj/
@@ -78,24 +78,26 @@ qed-.
 
 (* Basic_1: includes: pr0_lift pr2_lift *)
 (* Basic_2A1: includes: cpr_lift *)
-lemma cpm_lifts_sn: ∀n,h,G. d_liftable2_sn (cpm n h G).
+lemma cpm_lifts_sn: ∀n,h,G. d_liftable2_sn … lifts (λL. cpm h G L n).
 #n #h #G #K #T1 #T2 * #c #Hc #HT12 #b #f #L #HLK #U1 #HTU1
 elim (cpg_lifts_sn … HT12 … HLK … HTU1) -K -T1
 /3 width=5 by ex2_intro/
 qed-.
 
-lemma cpm_lifts_bi: ∀n,h,G. d_liftable2_bi (cpm n h G).
-/3 width=9 by cpm_lifts_sn, d_liftable2_sn_bi/ qed-.
+lemma cpm_lifts_bi: ∀n,h,G. d_liftable2_bi … lifts (λL. cpm h G L n).
+#n #h #G #K #T1 #T2 * /3 width=11 by cpg_lifts_bi, ex2_intro/
+qed-.
 
 (* Inversion lemmas with generic slicing for local environments *************)
 
 (* Basic_1: includes: pr0_gen_lift pr2_gen_lift *)
 (* Basic_2A1: includes: cpr_inv_lift1 *)
-lemma cpm_inv_lifts_sn: ∀n,h,G. d_deliftable2_sn (cpm n h G).
+lemma cpm_inv_lifts_sn: ∀n,h,G. d_deliftable2_sn … lifts (λL. cpm h G L n).
 #n #h #G #L #U1 #U2 * #c #Hc #HU12 #b #f #K #HLK #T1 #HTU1
 elim (cpg_inv_lifts_sn … HU12 … HLK … HTU1) -L -U1
 /3 width=5 by ex2_intro/
 qed-.
 
-lemma cpm_inv_lifts_bi: ∀n,h,G. d_deliftable2_bi (cpm n h G).
-/3 width=9 by cpm_inv_lifts_sn, d_deliftable2_sn_bi/ qed-.
+lemma cpm_inv_lifts_bi: ∀n,h,G. d_deliftable2_bi … lifts (λL. cpm h G L n).
+#n #h #G #L #U1 #U2 * /3 width=11 by cpg_inv_lifts_bi, ex2_intro/
+qed-.