milestone in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / csx_simple_theq.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_simple_theq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_simple_theq.ma
index cc286ae6a60a933c211e06a90b7021a7feec74a6..478f6fa0584c54a370b2493e6252707b0707a8d1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_simple_theq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_simple_theq.ma
@@ -24,10 +24,10 @@ include "basic_2/rt_computation/csx_csx.ma".
 
 (* Basic_1: was just: sn3_appl_appl *)
 (* Basic_2A1: was: csx_appl_simple_tsts *)
-lemma csx_appl_simple_theq: ∀h,o,G,L,V. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ → ∀T1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃T1⦄ →
-                            (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ⩳[h, o] T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T2⦄) →
-                            𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.T1⦄.
-#h #o #G #L #V #H @(csx_ind … H) -V
+lemma csx_appl_simple_theq: ∀h,G,L,V. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → ∀T1. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
+                            (∀T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ⩳ T2 → ⊥) → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T2⦄) →
+                            𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.T1⦄.
+#h #G #L #V #H @(csx_ind … H) -V
 #V #_ #IHV #T1 #H @(csx_ind … H) -T1
 #T1 #H1T1 #IHT1 #H2T1 #H3T1
 @csx_intro #X #HL #H
@@ -40,7 +40,7 @@ elim (tdneq_inv_pair … H) -H
   @IHV -IHV /4 width=3 by csx_cpx_trans, cpx_pair_sn/
 | -IHV -H1T1 #H1T10
   @(csx_cpx_trans … (ⓐV.T0)) /2 width=1 by cpx_flat/ -HLV0
-  elim (theq_dec h o T1 T0) #H2T10
+  elim (theq_dec T1 T0) #H2T10
   [ @IHT1 -IHT1 /4 width=5 by cpxs_strap2, cpxs_strap1, theq_canc_sn, simple_theq_repl_dx/
   | -IHT1 -H3T1 -H1T10 /3 width=1 by cpx_cpxs/
   ]