update in basic_2 and apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr.ma
index 8d50d4d4d38bd175e9d67e8e4976af5011eaef20..0e21c66879f7aaa355cee3d082cb6d98d7999caa 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnr.ma
@@ -12,21 +12,23 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/prednormal_4.ma".
+include "basic_2/notation/relations/prednormal_5.ma".
 include "basic_2/rt_transition/cpr.ma".
 
 (* NORMAL TERMS FOR CONTEXT-SENSITIVE R-TRANSITION **************************)
 
-definition cnr (h) (G) (L): predicate term ≝ NF … (cpm h G L 0) (eq …).
+definition cnr (h) (n) (G) (L): predicate term ≝
+           NF … (cpm h G L n) (eq …).
 
 interpretation
    "normality for context-sensitive r-transition (term)"
-   'PRedNormal h G L T = (cnr h G L T).
+   'PRedNormal h n G L T = (cnr h n G L T).
 
 (* Basic inversion lemmas ***************************************************)
 
 lemma cnr_inv_abst (h) (p) (G) (L):
-      ∀V,T. ❪G,L❫ ⊢ ➡[h] 𝐍❪ⓛ[p]V.T❫ → ∧∧ ❪G,L❫ ⊢ ➡[h] 𝐍❪V❫ & ❪G,L.ⓛV❫ ⊢ ➡[h] 𝐍❪T❫.
+      ∀V,T. ❪G,L❫ ⊢ ➡𝐍[h,0] ⓛ[p]V.T →
+      ∧∧ ❪G,L❫ ⊢ ➡𝐍[h,0] V & ❪G,L.ⓛV❫ ⊢ ➡𝐍[h,0] T.
 #h #p #G #L #V1 #T1 #HVT1 @conj
 [ #V2 #HV2 lapply (HVT1 (ⓛ[p]V2.T1) ?) -HVT1 /2 width=2 by cpr_pair_sn/ -HV2 #H destruct //
 | #T2 #HT2 lapply (HVT1 (ⓛ[p]V1.T2) ?) -HVT1 /2 width=2 by cpm_bind/ -HT2 #H destruct //
@@ -35,7 +37,8 @@ qed-.
 
 (* Basic_2A1: was: cnr_inv_abbr *)
 lemma cnr_inv_abbr_neg (h) (G) (L):
-      ∀V,T. ❪G,L❫ ⊢ ➡[h] 𝐍❪-ⓓV.T❫ → ∧∧ ❪G,L❫ ⊢ ➡[h] 𝐍❪V❫ & ❪G,L.ⓓV❫ ⊢ ➡[h] 𝐍❪T❫.
+      ∀V,T. ❪G,L❫ ⊢ ➡𝐍[h,0] -ⓓV.T →
+      ∧∧ ❪G,L❫ ⊢ ➡𝐍[h,0] V & ❪G,L.ⓓV❫ ⊢ ➡𝐍[h,0] T.
 #h #G #L #V1 #T1 #HVT1 @conj
 [ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2 by cpr_pair_sn/ -HV2 #H destruct //
 | #T2 #HT2 lapply (HVT1 (-ⓓV1.T2) ?) -HVT1 /2 width=2 by cpm_bind/ -HT2 #H destruct //
@@ -43,7 +46,8 @@ lemma cnr_inv_abbr_neg (h) (G) (L):
 qed-.
 
 (* Basic_2A1: was: cnr_inv_eps *)
-lemma cnr_inv_cast (h) (G) (L): ∀V,T. ❪G,L❫ ⊢ ➡[h] 𝐍❪ⓝV.T❫ → ⊥.
+lemma cnr_inv_cast (h) (G) (L):
+      ∀V,T. ❪G,L❫ ⊢ ➡𝐍[h,0] ⓝV.T → ⊥.
 #h #G #L #V #T #H lapply (H T ?) -H
 /2 width=4 by cpm_eps, discr_tpair_xy_y/
 qed-.
@@ -51,26 +55,28 @@ qed-.
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: nf2_sort *)
-lemma cnr_sort (h) (G) (L): ∀s. ❪G,L❫ ⊢ ➡[h] 𝐍❪⋆s❫.
+lemma cnr_sort (h) (G) (L):
+      ∀s. ❪G,L❫ ⊢ ➡𝐍[h,0] ⋆s.
 #h #G #L #s #X #H
 >(cpr_inv_sort1 … H) //
 qed.
 
-lemma cnr_gref (h) (G) (L): ∀l. ❪G,L❫ ⊢ ➡[h] 𝐍❪§l❫.
+lemma cnr_gref (h) (G) (L):
+      ∀l. ❪G,L❫ ⊢ ➡𝐍[h,0] §l.
 #h #G #L #l #X #H
 >(cpr_inv_gref1 … H) //
 qed.
 
 (* Basic_1: was: nf2_abst *)
 lemma cnr_abst (h) (p) (G) (L):
-      ∀W,T. ❪G,L❫ ⊢ ➡[h] 𝐍❪W❫ → ❪G,L.ⓛW❫ ⊢ ➡[h] 𝐍❪T❫ → ❪G,L❫ ⊢ ➡[h] 𝐍❪ⓛ[p]W.T❫.
+      ∀W,T. ❪G,L❫ ⊢ ➡𝐍[h,0] W → ❪G,L.ⓛW❫ ⊢ ➡𝐍[h,0] T → ❪G,L❫ ⊢ ➡𝐍[h,0] ⓛ[p]W.T.
 #h #p #G #L #W #T #HW #HT #X #H
 elim (cpm_inv_abst1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
 <(HW … HW0) -W0 <(HT … HT0) -T0 //
 qed.
 
 lemma cnr_abbr_neg (h) (G) (L):
-      ∀V,T. ❪G,L❫ ⊢ ➡[h] 𝐍❪V❫ → ❪G,L.ⓓV❫ ⊢ ➡[h] 𝐍❪T❫ → ❪G,L❫ ⊢ ➡[h] 𝐍❪-ⓓV.T❫.
+      ∀V,T. ❪G,L❫ ⊢ ➡𝐍[h,0] V → ❪G,L.ⓓV❫ ⊢ ➡𝐍[h,0] T → ❪G,L❫ ⊢ ➡𝐍[h,0] -ⓓV.T.
 #h #G #L #V #T #HV #HT #X #H
 elim (cpm_inv_abbr1 … H) -H *
 [ #V0 #T0 #HV0 #HT0 #H destruct