second recursive part of preservation finally proved!

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / unwind / sstas_sstas.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma b/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma
index e7e99c001b590878f671e3c1fe67569cf177079c..84b9412327283d0a750d687703c45061375645f3 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/unwind/sstas_sstas.ma
@@ -21,7 +21,7 @@ include "basic_2/unwind/sstas.ma".
 
 lemma sstas_inv_O: ∀h,g,L,T,U. ⦃h, L⦄ ⊢ T •*[g] U →
                    ∀T0. ⦃h, L⦄ ⊢ T •[g , 0] T0 → U = T.
-#h #g #L #T #U #H @(sstas_ind_alt … H) -T //
+#h #g #L #T #U #H @(sstas_ind_dx … H) -T //
 #T0 #U0 #l0 #HTU0 #_ #_ #T1 #HT01
 elim (ssta_mono … HTU0 … HT01) <plus_n_Sm #H destruct
 qed-.
@@ -30,8 +30,8 @@ qed-.
 
 lemma sstas_strip: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 →
                    ∀U2,l. ⦃h, L⦄ ⊢ T •[g, l] U2 →
-                   ⦃h, L⦄ ⊢ U1 •[g, l] U2 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1.
-#h #g #L #T #U1 #H1 @(sstas_ind_alt … H1) -T /2 width=1/
+                   T = U1 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1.
+#h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
 #T #U #l0 #HTU #HU1 #_ #U2 #l #H2
 elim (ssta_mono … H2 … HTU) -H2 -HTU #H1 #H2 destruct /2 width=1/
 qed-.
@@ -40,13 +40,15 @@ qed-.
 
 theorem sstas_trans: ∀h,g,L,T1,U. ⦃h, L⦄ ⊢ T1 •*[g] U →
                      ∀T2. ⦃h, L⦄ ⊢ U •*[g] T2 → ⦃h, L⦄ ⊢ T1 •*[g] T2.
-#h #g #L #T1 #U #H1 @(sstas_ind_alt … H1) -T1 // /3 width=4/
-qed-.
+/2 width=3/ qed-.
 
 theorem sstas_conf: ∀h,g,L,T,U1. ⦃h, L⦄ ⊢ T •*[g] U1 →
                     ∀U2. ⦃h, L⦄ ⊢ T •*[g] U2 →
                    ⦃h, L⦄ ⊢ U1 •*[g] U2 ∨ ⦃h, L⦄ ⊢ U2 •*[g] U1.
-#h #g #L #T #U1 #H1 @(sstas_ind_alt … H1) -T /2 width=1/
+#h #g #L #T #U1 #H1 @(sstas_ind_dx … H1) -T /2 width=1/
 #T #U #l #HTU #HU1 #IHU1 #U2 #H2
-elim (sstas_strip … H2 … HTU) -T /2 width=1/ -IHU1 /3 width=4/
+elim (sstas_strip … H2 … HTU) #H destruct
+[ -H2 -IHU1 /3 width=4/
+| -T /2 width=1/
+]
 qed-.