some restyling ...

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_theq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_theq.ma
index 58ee196139ccbdc68c1d9fb25f3fdc344ab856a6..5174890e003412e35653dbe8902b879457de567a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_theq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_theq.ma
@@ -21,7 +21,7 @@ include "basic_2/rt_computation/lpxs_cpxs.ma".
 
 (* Forward lemmas with head equivalence for terms ***************************)
 
-lemma cpxs_fwd_sort: ∀h,G,L,X2,s1. ⦃G, L⦄ ⊢ ⋆s1 ⬈*[h] X2 → ⋆s1 ⩳ X2.
+lemma cpxs_fwd_sort: ∀h,G,L,X2,s1. ⦃G,L⦄ ⊢ ⋆s1 ⬈*[h] X2 → ⋆s1 ⩳ X2.
 #h #G #L #X2 #s1 #H
 elim (cpxs_inv_sort1 … H) -H #s2 #H destruct //
 qed-.
@@ -30,8 +30,8 @@ qed-.
 (* Basic_2A1: was: cpxs_fwd_delta *)
 lemma cpxs_fwd_delta_drops: ∀h,I,G,L,K,V1,i. ⬇*[i] L ≘ K.ⓑ{I}V1 →
                             ∀V2. ⬆*[↑i] V1 ≘ V2 →
-                            ∀X2. ⦃G, L⦄ ⊢ #i ⬈*[h] X2 →
-                            ∨∨ #i ⩳ X2 | ⦃G, L⦄ ⊢ V2 ⬈*[h] X2.
+                            ∀X2. ⦃G,L⦄ ⊢ #i ⬈*[h] X2 →
+                            ∨∨ #i ⩳ X2 | ⦃G,L⦄ ⊢ V2 ⬈*[h] X2.
 #h #I #G #L #K #V1 #i #HLK #V2 #HV12 #X2 #H
 elim (cpxs_inv_lref1_drops … H) -H /2 width=1 by or_introl/
 * #I0 #K0 #V0 #U0 #HLK0 #HVU0 #HU0
@@ -40,8 +40,8 @@ lapply (drops_mono … HLK0 … HLK) -HLK0 #H destruct
 qed-.
 
 (* Basic_1: was just: pr3_iso_beta *)
-lemma cpxs_fwd_beta: ∀h,p,G,L,V,W,T,X2. ⦃G, L⦄ ⊢ ⓐV.ⓛ{p}W.T ⬈*[h] X2 →
-                     ∨∨ ⓐV.ⓛ{p}W.T ⩳ X2 | ⦃G, L⦄ ⊢ ⓓ{p}ⓝW.V.T ⬈*[h] X2.
+lemma cpxs_fwd_beta: ∀h,p,G,L,V,W,T,X2. ⦃G,L⦄ ⊢ ⓐV.ⓛ{p}W.T ⬈*[h] X2 →
+                     ∨∨ ⓐV.ⓛ{p}W.T ⩳ X2 | ⦃G,L⦄ ⊢ ⓓ{p}ⓝW.V.T ⬈*[h] X2.
 #h #p #G #L #V #W #T #X2 #H elim (cpxs_inv_appl1 … H) -H *
 [ #V0 #T0 #_ #_ #H destruct /2 width=1 by theq_pair, or_introl/
 | #b #W0 #T0 #HT0 #HU
@@ -53,9 +53,9 @@ lemma cpxs_fwd_beta: ∀h,p,G,L,V,W,T,X2. ⦃G, L⦄ ⊢ ⓐV.ⓛ{p}W.T ⬈*[h]
 ]
 qed-.
 
-lemma cpxs_fwd_theta: ∀h,p,G,L,V1,V,T,X2. ⦃G, L⦄ ⊢ ⓐV1.ⓓ{p}V.T ⬈*[h] X2 →
+lemma cpxs_fwd_theta: ∀h,p,G,L,V1,V,T,X2. ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}V.T ⬈*[h] X2 →
                       ∀V2. ⬆*[1] V1 ≘ V2 →
-                      ∨∨ ⓐV1.ⓓ{p}V.T ⩳ X2 | ⦃G, L⦄ ⊢ ⓓ{p}V.ⓐV2.T ⬈*[h] X2.
+                      ∨∨ ⓐV1.ⓓ{p}V.T ⩳ X2 | ⦃G,L⦄ ⊢ ⓓ{p}V.ⓐV2.T ⬈*[h] X2.
 #h #p #G #L #V1 #V #T #X2 #H #V2 #HV12
 elim (cpxs_inv_appl1 … H) -H *
 [ -HV12 #V0 #T0 #_ #_ #H destruct /2 width=1 by theq_pair, or_introl/
@@ -84,13 +84,13 @@ elim (cpxs_inv_appl1 … H) -H *
 ]
 qed-.
 
-lemma cpxs_fwd_cast: ∀h,G,L,W,T,X2. ⦃G, L⦄ ⊢ ⓝW.T ⬈*[h] X2 →
-                     ∨∨ ⓝW. T ⩳ X2 | ⦃G, L⦄ ⊢ T ⬈*[h] X2 | ⦃G, L⦄ ⊢ W ⬈*[h] X2.
+lemma cpxs_fwd_cast: ∀h,G,L,W,T,X2. ⦃G,L⦄ ⊢ ⓝW.T ⬈*[h] X2 →
+                     ∨∨ ⓝW. T ⩳ X2 | ⦃G,L⦄ ⊢ T ⬈*[h] X2 | ⦃G,L⦄ ⊢ W ⬈*[h] X2.
 #h #G #L #W #T #X2 #H
 elim (cpxs_inv_cast1 … H) -H /2 width=1 by or3_intro1, or3_intro2/ *
 #W0 #T0 #_ #_ #H destruct /2 width=1 by theq_pair, or3_intro0/
 qed-.
 
-lemma cpxs_fwd_cnx: ∀h,G,L,T1. ⦃G, L⦄ ⊢ ⬈[h] 𝐍⦃T1⦄ →
-                    ∀X2. ⦃G, L⦄ ⊢ T1 ⬈*[h] X2 → T1 ⩳ X2.
+lemma cpxs_fwd_cnx: ∀h,G,L,T1. ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃T1⦄ →
+                    ∀X2. ⦃G,L⦄ ⊢ T1 ⬈*[h] X2 → T1 ⩳ X2.
 /3 width=5 by cpxs_inv_cnx1, tdeq_theq/ qed-.