X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcpxs_tstc.ma;h=6f7bf603841e13c73fcfc536cf71784da6f6fe0e;hb=52e675f555f559c047d5449db7fc89a51b977d35;hp=ec36d47f1432e71b0685fbf8d2607ed5e4b7cf60;hpb=62211b3b2d76ba387663c9e553fbe4d2dbd92c82;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma
index ec36d47f1..6f7bf6038 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_tstc.ma
@@ -19,13 +19,13 @@ include "basic_2/computation/lpxs_cpxs.ma".
 
 (* Forward lemmas involving same top term constructor ***********************)
 
-lemma cpxs_fwd_cnx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ 𝐍[h, g]⦃T⦄ → ∀U. ⦃G, L⦄ ⊢ T ➡*[h, g] U → T ≃ U.
+lemma cpxs_fwd_cnx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ➡[h, g] 𝐍⦃T⦄ → ∀U. ⦃G, L⦄ ⊢ T ➡*[h, g] U → T ≂ U.
 #h #g #G #L #T #HT #U #H
 >(cpxs_inv_cnx1 … H HT) -G -L -T //
 qed-.
 
 lemma cpxs_fwd_sort: ∀h,g,G,L,U,k. ⦃G, L⦄ ⊢ ⋆k ➡*[h, g] U →
-                     ⋆k ≃ U ∨ ⦃G, L⦄ ⊢ ⋆(next h k) ➡*[h, g] U.
+                     ⋆k ≂ U ∨ ⦃G, L⦄ ⊢ ⋆(next h k) ➡*[h, g] U.
 #h #g #G #L #U #k #H
 elim (cpxs_inv_sort1 … H) -H #n #l generalize in match k; -k @(nat_ind_plus … n) -n
 [ #k #_ #H -l destruct /2 width=1 by or_introl/
@@ -34,7 +34,7 @@ elim (cpxs_inv_sort1 … H) -H #n #l generalize in match k; -k @(nat_ind_plus 
   elim (IHn … Hnl) -IHn
   [ #H lapply (tstc_inv_atom1 … H) -H #H >H -H /2 width=1 by or_intror/
   | generalize in match Hnl; -Hnl @(nat_ind_plus … n) -n
-    /4 width=3 by cpxs_strap2, cpx_sort, or_intror/
+    /4 width=3 by cpxs_strap2, cpx_st, or_intror/
   | >iter_SO >iter_n_Sm //
   ]
 ]
@@ -42,7 +42,7 @@ qed-.
 
 (* Basic_1: was just: pr3_iso_beta *)
 lemma cpxs_fwd_beta: ∀h,g,a,G,L,V,W,T,U. ⦃G, L⦄ ⊢ ⓐV.ⓛ{a}W.T ➡*[h, g] U →
-                     ⓐV.ⓛ{a}W.T ≃ U ∨ ⦃G, L⦄ ⊢ ⓓ{a}ⓝW.V.T ➡*[h, g] U.
+                     ⓐV.ⓛ{a}W.T ≂ U ∨ ⦃G, L⦄ ⊢ ⓓ{a}ⓝW.V.T ➡*[h, g] U.
 #h #g #a #G #L #V #W #T #U #H
 elim (cpxs_inv_appl1 … H) -H *
 [ #V0 #T0 #_ #_ #H destruct /2 width=1 by tstc_pair, or_introl/
@@ -59,16 +59,16 @@ qed-.
 lemma cpxs_fwd_delta: ∀h,g,I,G,L,K,V1,i. ⇩[i] L ≡ K.ⓑ{I}V1 →
                       ∀V2. ⇧[0, i + 1] V1 ≡ V2 →
                       ∀U. ⦃G, L⦄ ⊢ #i ➡*[h, g] U →
-                      #i ≃ U ∨ ⦃G, L⦄ ⊢ V2 ➡*[h, g] U.
+                      #i ≂ U ∨ ⦃G, L⦄ ⊢ V2 ➡*[h, g] U.
 #h #g #I #G #L #K #V1 #i #HLK #V2 #HV12 #U #H
 elim (cpxs_inv_lref1 … H) -H /2 width=1 by or_introl/
 * #I0 #K0 #V0 #U0 #HLK0 #HVU0 #HU0
-lapply (ldrop_mono … HLK0 … HLK) -HLK0 #H destruct
-/4 width=10 by cpxs_lift, ldrop_fwd_drop2, or_intror/
+lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct
+/4 width=10 by cpxs_lift, drop_fwd_drop2, or_intror/
 qed-.
 
 lemma cpxs_fwd_theta: ∀h,g,a,G,L,V1,V,T,U. ⦃G, L⦄ ⊢ ⓐV1.ⓓ{a}V.T ➡*[h, g] U →
-                      ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1.ⓓ{a}V.T ≃ U ∨
+                      ∀V2. ⇧[0, 1] V1 ≡ V2 → ⓐV1.ⓓ{a}V.T ≂ U ∨
                       ⦃G, L⦄ ⊢ ⓓ{a}V.ⓐV2.T ➡*[h, g] U.
 #h #g #a #G #L #V1 #V #T #U #H #V2 #HV12
 elim (cpxs_inv_appl1 … H) -H *
@@ -88,10 +88,10 @@ elim (cpxs_inv_appl1 … H) -H *
   elim (cpxs_inv_abbr1 … HT0) -HT0 *
   [ #V5 #T5 #HV5 #HT5 #H destruct
     lapply (cpxs_lift … HV13 (L.ⓓV) … HV12 … HV34) -V1 -V3
-    /3 width=2 by cpxs_flat, cpxs_bind, ldrop_drop/
+    /3 width=2 by cpxs_flat, cpxs_bind, drop_drop/
   | #X #HT1 #H #H0 destruct
     elim (lift_inv_bind1 … H) -H #V5 #T5 #HV05 #HT05 #H destruct
-    lapply (cpxs_lift … HV13 (L.ⓓV0) … HV12 … HV34) -V3 /2 width=2 by ldrop_drop/ #HV24
+    lapply (cpxs_lift … HV13 (L.ⓓV0) … HV12 … HV34) -V3 /2 width=2 by drop_drop/ #HV24
     @(cpxs_trans … (+ⓓV.ⓐV2.ⓓ{b}V5.T5)) [ /3 width=1 by cpxs_flat_dx, cpxs_bind_dx/ ] -T
     @(cpxs_strap2 … (ⓐV1.ⓓ{b}V0.T0)) [ /4 width=7 by cpx_zeta, lift_bind, lift_flat/ ] -V -V5 -T5
     @(cpxs_strap2 … (ⓓ{b}V0.ⓐV2.T0)) /3 width=3 by cpxs_pair_sn, cpxs_bind_dx, cpr_cpx, cpr_theta/
@@ -100,7 +100,7 @@ elim (cpxs_inv_appl1 … H) -H *
 qed-.
 
 lemma cpxs_fwd_cast: ∀h,g,G,L,W,T,U. ⦃G, L⦄ ⊢ ⓝW.T ➡*[h, g] U →
-                     ∨∨ ⓝW. T ≃ U | ⦃G, L⦄ ⊢ T ➡*[h, g] U | ⦃G, L⦄ ⊢ W ➡*[h, g] U.
+                     ∨∨ ⓝW. T ≂ U | ⦃G, L⦄ ⊢ T ➡*[h, g] U | ⦃G, L⦄ ⊢ W ➡*[h, g] U.
 #h #g #G #L #W #T #U #H
 elim (cpxs_inv_cast1 … H) -H /2 width=1 by or3_intro1, or3_intro2/ *
 #W0 #T0 #_ #_ #H destruct /2 width=1 by tstc_pair, or3_intro0/