lambdadelta

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr.ma
index 7bd1ad6d1dcef53157ff45e3614e39e2ef555cfd..821d74c7a2b83eaf7c96f62793ac6e0a5fba655b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cnr.ma
@@ -12,6 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/notation/relations/normal_2.ma".
 include "basic_2/reduction/cpr.ma".
 
 (* CONTEXT-SENSITIVE NORMAL TERMS *******************************************)
@@ -51,7 +52,7 @@ lemma cnr_inv_zeta: ∀L,V,T. L ⊢ 𝐍⦃+ⓓV.T⦄ → ⊥.
   lapply (H U ?) -H /2 width=3/ #H destruct
   elim (lift_inv_pair_xy_y … HTU)
 | #HT
-  elim (cpss_delift (⋆) V T (⋆. ⓓV) 0 ?) // #T2 #T1 #HT2 #HT12
+  elim (cpr_delift (⋆) V T (⋆. ⓓV) 0) // #T2 #T1 #HT2 #HT12
   lapply (H (+ⓓV.T2) ?) -H /4 width=1/ -HT2 #H destruct /3 width=2/
 ]
 qed-.
@@ -63,7 +64,7 @@ lemma cnr_inv_appl: ∀L,V,T. L ⊢ 𝐍⦃ⓐV.T⦄ → ∧∧ L ⊢ 𝐍⦃V
 | generalize in match HVT1; -HVT1 elim T1 -T1 * // #a * #W1 #U1 #_ #_ #H
   [ elim (lift_total V1 0 1) #V2 #HV12
     lapply (H (ⓓ{a}W1.ⓐV2.U1) ?) -H /3 width=3/ -HV12 #H destruct
-  | lapply (H (ⓓ{a}V1.U1) ?) -H /3 width=1/ #H destruct
+  | lapply (H (ⓓ{a}ⓝW1.V1.U1) ?) -H /3 width=1/ #H destruct
 ]
 qed-.
 
@@ -81,16 +82,16 @@ lemma cnr_sort: ∀L,k. L ⊢ 𝐍⦃⋆k⦄.
 qed.
 
 (* Basic_1: was: nf2_abst *)
-lemma cnr_abst: ∀a,I,L,V,W,T. L ⊢ 𝐍⦃W⦄ → L. ⓑ{I} V ⊢ 𝐍⦃T⦄ → L ⊢ 𝐍⦃ⓛ{a}W.T⦄.
-#a #I #L #V #W #T #HW #HT #X #H
-elim (cpr_fwd_abst1 … H I V) -H #W0 #T0 #HW0 #HT0 #H destruct
+lemma cnr_abst: ∀a,L,W,T. L ⊢ 𝐍⦃W⦄ → L.ⓛW ⊢ 𝐍⦃T⦄ → L ⊢ 𝐍⦃ⓛ{a}W.T⦄.
+#a #L #W #T #HW #HT #X #H
+elim (cpr_inv_abst1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
 >(HW … HW0) -W0 >(HT … HT0) -T0 //
 qed.
 
 (* Basic_1: was only: nf2_appl_lref *)
 lemma cnr_appl_simple: ∀L,V,T. L ⊢ 𝐍⦃V⦄ → L ⊢ 𝐍⦃T⦄ → 𝐒⦃T⦄ → L ⊢ 𝐍⦃ⓐV.T⦄.
 #L #V #T #HV #HT #HS #X #H
-elim (cpr_inv_appl1_simple … H ?) -H // #V0 #T0 #HV0 #HT0 #H destruct
+elim (cpr_inv_appl1_simple … H) -H // #V0 #T0 #HV0 #HT0 #H destruct
 >(HV … HV0) -V0 >(HT … HT0) -T0 //
 qed.