X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fcomputation%2Flpxs.ma;h=ee557e4385fa4038a8df142dab4d8079c0f79c8a;hb=9ed13b93cd1d7d75d65f1f063b6b4bf27d863f72;hp=35a8cb4829f5db8de2943380739bff31c1813bc8;hpb=82500a9ceb53e1af0263c22afbd5954fa3a83190;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma
index 35a8cb482..ee557e438 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/lpxs.ma
@@ -43,19 +43,19 @@ qed-.
 (* Basic properties *********************************************************)
 
 lemma lprs_lpxs: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡* L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
-/3 width=3/ qed.
+/3 width=3 by lpr_lpx, monotonic_TC/ qed.
 
 lemma lpx_lpxs: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
-/2 width=1/ qed.
+/2 width=1 by inj/ qed.
 
 lemma lpxs_refl: ∀h,g,G,L. ⦃G, L⦄ ⊢ ➡*[h, g] L.
-/2 width=1/ qed.
+/2 width=1 by lprs_lpxs/ qed.
 
 lemma lpxs_strap1: ∀h,g,G,L1,L,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L → ⦃G, L⦄ ⊢ ➡[h, g] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
-/2 width=3/ qed.
+/2 width=3 by step/ qed.
 
 lemma lpxs_strap2: ∀h,g,G,L1,L,L2. ⦃G, L1⦄ ⊢ ➡[h, g] L → ⦃G, L⦄ ⊢ ➡*[h, g] L2 → ⦃G, L1⦄ ⊢ ➡*[h, g] L2.
-/2 width=3/ qed.
+/2 width=3 by TC_strap/ qed.
 
 lemma lpxs_pair_refl: ∀h,g,G,L1,L2. ⦃G, L1⦄ ⊢ ➡*[h, g] L2 → ∀I,V. ⦃G, L1.ⓑ{I}V⦄ ⊢ ➡*[h, g] L2.ⓑ{I}V.
 /2 width=1 by TC_lpx_sn_pair_refl/ qed.