X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Fcsx_alt.ma;h=df23e1f2ab9374774ace93fe4073ae840611560a;hb=b5d702735754632652b2659c425dd67d7f92f24b;hp=7c95fed6ed5cbf535c7ee4e551289536367163c7;hpb=c28e3d93b588796bfbbfd6b2ec9dd86f405b2b00;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_alt.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_alt.ma
index 7c95fed6e..df23e1f2a 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csx_alt.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csx_alt.ma
@@ -33,31 +33,35 @@ lemma csxa_ind: ∀h,g,G,L. ∀R:predicate term.
                       (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
                 ) →
                 ∀T. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T → R T.
-#h #g #G #L #R #H0 #T1 #H elim H -T1 #T1 #HT1 #IHT1
-@H0 -H0 /3 width=1/ -IHT1 /4 width=1/
+#h #g #G #L #R #H0 #T1 #H elim H -T1 /5 width=1 by SN_intro/
 qed-.
 
 (* Basic properties *********************************************************)
 
+lemma csx_intro_cprs: ∀h,g,G,L,T1.
+                         (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, g] T2) →
+                      ⦃G, L⦄ ⊢ ⬊*[h, g] T1.
+/4 width=1 by cpx_cpxs, csx_intro/ qed.
+
 (* Basic_1: was just: sn3_intro *)
 lemma csxa_intro: ∀h,g,G,L,T1.
                   (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2) →
                   ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1.
-/4 width=1/ qed.
+/4 width=1 by SN_intro/ qed.
 
 fact csxa_intro_aux: ∀h,g,G,L,T1. (
                         ∀T,T2. ⦃G, L⦄ ⊢ T ➡*[h, g] T2 → T1 = T → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2
                      ) → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1.
-/4 width=3/ qed-.
+/4 width=3 by csxa_intro/ qed-.
 
 (* Basic_1: was just: sn3_pr3_trans (old version) *)
 lemma csxa_cpxs_trans: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T1 →
                        ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T2.
 #h #g #G #L #T1 #H elim H -T1 #T1 #HT1 #IHT1 #T2 #HLT12
 @csxa_intro #T #HLT2 #HT2
-elim (term_eq_dec T1 T2) #HT12
-[ -IHT1 -HLT12 destruct /3 width=1/
-| -HT1 -HT2 /3 width=4/
+elim (eq_term_dec T1 T2) #HT12
+[ -IHT1 -HLT12 destruct /3 width=1 by/
+| -HT1 -HT2 /3 width=4 by/
 qed.
 
 (* Basic_1: was just: sn3_pr2_intro (old version) *)
@@ -69,9 +73,9 @@ lemma csxa_intro_cpx: ∀h,g,G,L,T1. (
 [ -H #H destruct #H
   elim H //
 | #T0 #T #HLT1 #HLT2 #IHT #HT10 #HT12 destruct
-  elim (term_eq_dec T0 T) #HT0
-  [ -HLT1 -HLT2 -H /3 width=1/
-  | -IHT -HT12 /4 width=3/
+  elim (eq_term_dec T0 T) #HT0
+  [ -HLT1 -HLT2 -H /3 width=1 by/
+  | -IHT -HT12 /4 width=3 by csxa_cpxs_trans/
   ]
 ]
 qed.
@@ -79,17 +83,17 @@ qed.
 (* Main properties **********************************************************)
 
 theorem csx_csxa: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T.
-#h #g #G #L #T #H @(csx_ind … H) -T /4 width=1/
+#h #g #G #L #T #H @(csx_ind … H) -T /4 width=1 by csxa_intro_cpx/
 qed.
 
 theorem csxa_csx: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ ⬊⬊*[h, g] T → ⦃G, L⦄ ⊢ ⬊*[h, g] T.
-#h #g #G #L #T #H @(csxa_ind … H) -T /4 width=1/
+#h #g #G #L #T #H @(csxa_ind … H) -T /4 width=1 by cpx_cpxs, csx_intro/
 qed.
 
 (* Basic_1: was just: sn3_pr3_trans *)
 lemma csx_cpxs_trans: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ ⬊*[h, g] T1 →
                       ∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → ⦃G, L⦄ ⊢ ⬊*[h, g] T2.
-#h #g #G #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2 // /2 width=3 by csx_cpx_trans/
+#h #g #G #L #T1 #HT1 #T2 #H @(cpxs_ind … H) -T2 /2 width=3 by csx_cpx_trans/
 qed-.
 
 (* Main eliminators *********************************************************)
@@ -99,6 +103,5 @@ lemma csx_ind_alt: ∀h,g,G,L. ∀R:predicate term.
                          (∀T2. ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2 → (T1 = T2 → ⊥) → R T2) → R T1
                    ) →
                    ∀T. ⦃G, L⦄ ⊢ ⬊*[h, g] T → R T.
-#h #g #G #L #R #H0 #T1 #H @(csxa_ind … (csx_csxa … H)) -T1 #T1 #HT1 #IHT1
-@H0 -H0 /2 width=1/ -HT1 /3 width=1/
+#h #g #G #L #R #H0 #T1 #H @(csxa_ind … (csx_csxa … H)) -T1 /4 width=1 by csxa_csx/
 qed-.