- lfpxs based on tc_lfxs

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma
index 7ca826d116941f719be727e7bf8f347191509bde..9664ec0a3256d559b960a7c2c2afa4f593d2f26b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lfsx_lfsx.ma
@@ -20,6 +20,7 @@ include "basic_2/rt_computation/lfsx.ma".
 
 (* Advanced properties ******************************************************)
 
+(* Basic_2A1: uses: lsx_lleq_trans *)
 lemma lfsx_lfdeq_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
                         ∀L2. L1 ≡[h, o, T] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
 #h #o #G #L1 #T #H @(lfsx_ind … H) -L1
@@ -28,10 +29,16 @@ lemma lfsx_lfdeq_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
 /4 width=5 by lfdeq_repl/
 qed-.
 
+(* Basic_2A1: uses: lsx_lpx_trans *)
+lemma lfsx_lfpx_trans: ∀h,o,G,L1,T. G ⊢ ⬈*[h, o, T] 𝐒⦃L1⦄ →
+                       ∀L2. ⦃G, L1⦄ ⊢ ⬈[h, T] L2 → G ⊢ ⬈*[h, o, T] 𝐒⦃L2⦄.
+#h #o #G #L1 #T #H @(lfsx_ind … H) -L1 #L1 #HL1 #IHL1 #L2 #HL12
+elim (lfdeq_dec h o L1 L2 T) /3 width=4 by lfsx_lfdeq_trans, lfxs_refl/
+qed-.
+
 (* Advanced forward lemmas **************************************************)
 
-(* Basic_2A1: includes: lsx_fwd_bind_sn lsx_fwd_flat_sn *)
-(* Basic_2A1: was: lsx_fwd_pair_sn *)
+(* Basic_2A1: uses: lsx_fwd_pair_sn lsx_fwd_bind_sn lsx_fwd_flat_sn *)
 lemma lfsx_fwd_pair_sn: ∀h,o,I,G,L,V,T. G ⊢ ⬈*[h, o, ②{I}V.T] 𝐒⦃L⦄ →
                         G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄.
 #h #o #I #G #L #V #T #H @(lfsx_ind … H) -L
@@ -40,8 +47,7 @@ lemma lfsx_fwd_pair_sn: ∀h,o,I,G,L,V,T. G ⊢ ⬈*[h, o, ②{I}V.T] 𝐒⦃L
 /6 width=4 by lfsx_lfdeq_trans, lfdeq_trans, lfdeq_fwd_pair_sn/
 qed-.
 
-
-(* Basic_2A1: was: lsx_fwd_flat_dx *)
+(* Basic_2A1: uses: lsx_fwd_flat_dx *)
 lemma lfsx_fwd_flat_dx: ∀h,o,I,G,L,V,T. G ⊢ ⬈*[h, o, ⓕ{I}V.T] 𝐒⦃L⦄ →
                         G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
 #h #o #I #G #L #V #T #H @(lfsx_ind … H) -L
@@ -52,7 +58,7 @@ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-(* Basic_2A1: was: lsx_inv_flat *)
+(* Basic_2A1: uses: lsx_inv_flat *)
 lemma lfsx_inv_flat: ∀h,o,I,G,L,V,T. G ⊢ ⬈*[h, o, ⓕ{I}V.T] 𝐒⦃L⦄ →
                      G ⊢ ⬈*[h, o, V] 𝐒⦃L⦄ ∧ G ⊢ ⬈*[h, o, T] 𝐒⦃L⦄.
 /3 width=3 by lfsx_fwd_pair_sn, lfsx_fwd_flat_dx, conj/ qed-.