some restyling ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lpx.ma
index 77cf480fab098688224d2e2544ffb2176052cc4c..ed06dcdea0abdbe0ba42d1754f11ee621555d14b 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lpx.ma
@@ -19,16 +19,16 @@ include "basic_2/rt_computation/csx_cpxs.ma".
 
 (* Properties with unbound parallel rt-transition on all entries ************)
 
-lemma csx_lpx_conf: ∀h,G,L1,T. ⦃G, L1⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →
-                    ∀L2. ⦃G, L1⦄ ⊢ ⬈[h] L2 → ⦃G, L2⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
+lemma csx_lpx_conf: ∀h,G,L1,T. ⦃G,L1⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ →
+                    ∀L2. ⦃G,L1⦄ ⊢ ⬈[h] L2 → ⦃G,L2⦄ ⊢ ⬈*[h] 𝐒⦃T⦄.
 #h #G #L1 #T #H @(csx_ind_cpxs … H) -T
 /4 width=3 by csx_intro, lpx_cpx_trans/
 qed-.
 
 (* Advanced properties ******************************************************)
 
-lemma csx_abst: ∀h,p,G,L,W. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃W⦄ →
-                ∀T. ⦃G, L.ⓛW⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓛ{p}W.T⦄.
+lemma csx_abst: ∀h,p,G,L,W. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃W⦄ →
+                ∀T. ⦃G,L.ⓛW⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓛ{p}W.T⦄.
 #h #p #G #L #W #HW
 @(csx_ind … HW) -W #W #_ #IHW #T #HT
 @(csx_ind … HT) -T #T #HT #IHT
@@ -42,8 +42,8 @@ elim (tdneq_inv_pair  … H2) -H2
 ]
 qed.
 
-lemma csx_abbr: ∀h,p,G,L,V. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ →
-                ∀T. ⦃G, L.ⓓV⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}V.T⦄.
+lemma csx_abbr: ∀h,p,G,L,V. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ →
+                ∀T. ⦃G,L.ⓓV⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}V.T⦄.
 #h #p #G #L #V #HV
 @(csx_ind … HV) -V #V #_ #IHV #T #HT
 @(csx_ind_cpxs … HT) -T #T #HT #IHT
@@ -60,8 +60,8 @@ elim (cpx_inv_abbr1 … H1) -H1 *
 ]
 qed.
 
-fact csx_appl_theta_aux: ∀h,p,G,L,U. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ → ∀V1,V2. ⬆*[1] V1 ≘ V2 →
-                         ∀V,T. U = ⓓ{p}V.ⓐV2.T → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV1.ⓓ{p}V.T⦄.
+fact csx_appl_theta_aux: ∀h,p,G,L,U. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃U⦄ → ∀V1,V2. ⬆*[1] V1 ≘ V2 →
+                         ∀V,T. U = ⓓ{p}V.ⓐV2.T → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV1.ⓓ{p}V.T⦄.
 #h #p #G #L #X #H
 @(csx_ind_cpxs … H) -X #X #HVT #IHVT #V1 #V2 #HV12 #V #T #H destruct
 lapply (csx_fwd_pair_sn … HVT) #HV
@@ -94,6 +94,6 @@ elim (cpx_inv_appl1 … HL) -HL *
 ]
 qed-.
 
-lemma csx_appl_theta: ∀h,p,G,L,V,V2,T. ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}V.ⓐV2.T⦄ →
-                      ∀V1. ⬆*[1] V1 ≘ V2 → ⦃G, L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV1.ⓓ{p}V.T⦄.
+lemma csx_appl_theta: ∀h,p,G,L,V,V2,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓓ{p}V.ⓐV2.T⦄ →
+                      ∀V1. ⬆*[1] V1 ≘ V2 → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓐV1.ⓓ{p}V.T⦄.
 /2 width=5 by csx_appl_theta_aux/ qed.