milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubsx_rdsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubsx_rdsx.ma
index 52454a2accf4baddc35b3e0f9523b3da7c804e56..70ba811a931419615ac2ec7e1de8553255473449 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubsx_rdsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lsubsx_rdsx.ma
@@ -21,10 +21,11 @@ include "basic_2/rt_computation/lsubsx.ma".
 (* Properties with strongly normalizing referred local environments *********)
 
 (* Basic_2A1: uses: lsx_cpx_trans_lcosx *)
-lemma rdsx_cpx_trans_lsubsx (h) (o): ∀G,L0,T1,T2. ⦃G, L0⦄ ⊢ T1 ⬈[h] T2 →
-                                     ∀f,L. G ⊢ L0 ⊆ⓧ[h, o, f] L →
-                                     G ⊢ ⬈*[h, o, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, o, T2] 𝐒⦃L⦄.
-#h #o #G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2 //
+lemma rdsx_cpx_trans_lsubsx (h):
+      ∀G,L0,T1,T2. ⦃G, L0⦄ ⊢ T1 ⬈[h] T2 →
+      ∀f,L. G ⊢ L0 ⊆ⓧ[h, f] L →
+      G ⊢ ⬈*[h, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, T2] 𝐒⦃L⦄.
+#h #G #L0 #T1 #T2 #H @(cpx_ind … H) -G -L0 -T1 -T2 //
 [ #I0 #G #K0 #V1 #V2 #W2 #_ #IH #HVW2 #g #L #HK0 #HL
   elim (lsubsx_inv_pair_sn_gen … HK0) -HK0 *
   [ #f #K #HK0 #H1 #H2 destruct
@@ -61,13 +62,15 @@ qed-.
 (* Advanced properties of strongly normalizing referred local environments **)
 
 (* Basic_2A1: uses: lsx_cpx_trans_O *)
-lemma rdsx_cpx_trans (h) (o): ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 →
-                              G ⊢ ⬈*[h, o, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, o, T2] 𝐒⦃L⦄.
+lemma rdsx_cpx_trans (h):
+      ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈[h] T2 →
+      G ⊢ ⬈*[h, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, T2] 𝐒⦃L⦄.
 /3 width=6 by rdsx_cpx_trans_lsubsx, lsubsx_refl/ qed-.
 
-lemma rdsx_cpxs_trans (h) (o): ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
-                               G ⊢ ⬈*[h, o, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, o, T2] 𝐒⦃L⦄.
-#h #o #G #L #T1 #T2 #H
+lemma rdsx_cpxs_trans (h):
+      ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬈*[h] T2 →
+      G ⊢ ⬈*[h, T1] 𝐒⦃L⦄ → G ⊢ ⬈*[h, T2] 𝐒⦃L⦄.
+#h #G #L #T1 #T2 #H
 @(cpxs_ind_dx ???????? H) -T1 //
 /3 width=3 by rdsx_cpx_trans/
 qed-.