milestone in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma
index 169970ed12ca49d1f68b9353850544fdcd89a787..b969425727c0842eb4c1d6f8fa4fb63e5e0134bb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma
@@ -19,9 +19,9 @@ include "basic_2/rt_computation/csx_csx.ma".
 
 (* Advanced properties ******************************************************)
 
-fact csx_appl_beta_aux: ∀h,o,p,G,L,U1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U1⦄ →
-                        ∀V,W,T1. U1 = ⓓ{p}ⓝW.V.T1 → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.ⓛ{p}W.T1⦄.
-#h #o #p #G #L #X #H @(csx_ind … H) -X
+fact csx_appl_beta_aux: ∀h,p,G,L,U1. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃U1⦄ →
+                        ∀V,W,T1. U1 = ⓓ{p}ⓝW.V.T1 → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.ⓛ{p}W.T1⦄.
+#h #p #G #L #X #H @(csx_ind … H) -X
 #X #HT1 #IHT1 #V #W #T1 #H1 destruct
 @csx_intro #X #H1 #H2
 elim (cpx_inv_appl1 … H1) -H1 *
@@ -42,23 +42,23 @@ elim (cpx_inv_appl1 … H1) -H1 *
 qed-.
 
 (* Basic_1: was just: sn3_beta *)
-lemma csx_appl_beta: ∀h,o,p,G,L,V,W,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓓ{p}ⓝW.V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.ⓛ{p}W.T⦄.
+lemma csx_appl_beta: ∀h,p,G,L,V,W,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}ⓝW.V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV.ⓛ{p}W.T⦄.
 /2 width=3 by csx_appl_beta_aux/ qed.
 
 (* Advanced forward lemmas **************************************************)
 
-fact csx_fwd_bind_dx_unit_aux: ∀h,o,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U⦄ →
-                               ∀p,I,J,V,T. U = ⓑ{p,I}V.T → ⦃G, L.ⓤ{J}⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
-#h #o #G #L #U #H elim H -H #U0 #_ #IH #p #I #J #V #T #H destruct
+fact csx_fwd_bind_dx_unit_aux: ∀h,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ →
+                               ∀p,I,J,V,T. U = ⓑ{p,I}V.T → ⦃G, L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+#h #G #L #U #H elim H -H #U0 #_ #IH #p #I #J #V #T #H destruct
 @csx_intro #T2 #HLT2 #HT2
 @(IH (ⓑ{p,I}V.T2)) -IH /2 width=4 by cpx_bind_unit/ -HLT2
 #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
 qed-.
 
-lemma csx_fwd_bind_dx_unit: ∀h,o,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓑ{p,I}V.T⦄ →
-                            ∀J. ⦃G, L.ⓤ{J}⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
+lemma csx_fwd_bind_dx_unit: ∀h,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
+                            ∀J. ⦃G, L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
 /2 width=6 by csx_fwd_bind_dx_unit_aux/ qed-.
 
-lemma csx_fwd_bind_unit: ∀h,o,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓑ{p,I}V.T⦄ →
-                         ∀J. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃V⦄ ∧ ⦃G, L.ⓤ{J}⦄ ⊢ ⬈*[h, o] 𝐒⦃T⦄.
+lemma csx_fwd_bind_unit: ∀h,p,I,G,L,V,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓑ{p,I}V.T⦄ →
+                         ∀J. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ ∧ ⦃G, L.ⓤ{J}⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
 /3 width=4 by csx_fwd_pair_sn, csx_fwd_bind_dx_unit, conj/ qed-.