partial commit: just the components before "static" ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cpxs_lift.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
index 2e86e82f4da3ad89e767f535e399c8c585d8c9ed..7bba480e4a42a78575b9fc127a8966c7a2f80bca 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_lift.ma
@@ -21,8 +21,8 @@ include "basic_2/computation/cpxs.ma".
 (* Advanced properties ******************************************************)
 
 lemma cpxs_delta: ∀h,g,I,L,K,V,V2,i.
-                  ⇩[0, i] L ≡ K. ⓑ{I}V → ⦃h, K⦄ ⊢ V ➡*[g] V2 →
-                  ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃h, L⦄ ⊢ #i ➡*[g] W2.
+                  ⇩[0, i] L ≡ K. ⓑ{I}V → ⦃h, K⦄ ⊢ V ➡*[h, g] V2 →
+                  ∀W2. ⇧[0, i + 1] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡*[h, g] W2.
 #h #g #I #L #K #V #V2 #i #HLK #H elim H -V2 [ /3 width=9/ ]
 #V1 #V2 #_ #HV12 #IHV1 #W2 #HVW2
 lapply (ldrop_fwd_ldrop2 … HLK) -HLK #HLK
@@ -31,9 +31,9 @@ qed.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpxs_inv_lref1: ∀h,g,L,T2,i. ⦃h, L⦄ ⊢ #i ➡*[g] T2 →
+lemma cpxs_inv_lref1: ∀h,g,L,T2,i. ⦃G, L⦄ ⊢ #i ➡*[h, g] T2 →
                       T2 = #i ∨
-                      ∃∃I,K,V1,T1. ⇩[0, i] L ≡ K.ⓑ{I}V1 & ⦃h, K⦄ ⊢ V1 ➡*[g] T1 &
+                      ∃∃I,K,V1,T1. ⇩[0, i] L ≡ K.ⓑ{I}V1 & ⦃h, K⦄ ⊢ V1 ➡*[h, g] T1 &
                                    ⇧[0, i + 1] T1 ≡ T2.
 #h #g #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1/
 #T #T2 #_ #HT2 *
@@ -57,9 +57,9 @@ qed-.
 
 (* Properties on supclosure *************************************************)
 
-lemma fsupq_cpxs_trans: ∀h,g,L1,L2,T2,U2. ⦃h, L2⦄ ⊢ T2 ➡*[g] U2 →
+lemma fsupq_cpxs_trans: ∀h,g,L1,L2,T2,U2. ⦃h, L2⦄ ⊢ T2 ➡*[h, g] U2 →
                         ∀T1. ⦃L1, T1⦄ ⊃⸮ ⦃L2, T2⦄ →
-                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡*[g] U1 & ⦃L1, U1⦄ ⊃* ⦃L2, U2⦄.
+                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃L1, U1⦄ ⊃* ⦃L2, U2⦄.
 #h #g #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 [ /3 width=3/ ]
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1
 elim (fsupq_cpx_trans … HT1 … HT2) -T #T #HT1 #HT2
@@ -67,8 +67,8 @@ elim (IHTU2 … HT2) -T2 /3 width=3/
 qed-.
 
 lemma fsups_cpxs_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃* ⦃L2, T2⦄ →
-                        ∀U2. ⦃h, L2⦄ ⊢ T2 ➡*[g] U2 →
-                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡*[g] U1 & ⦃L1, U1⦄ ⊃* ⦃L2, U2⦄.
+                        ∀U2. ⦃h, L2⦄ ⊢ T2 ➡*[h, g] U2 →
+                        ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡*[h, g] U1 & ⦃L1, U1⦄ ⊃* ⦃L2, U2⦄.
 #h #g #L1 #L2 #T1 #T2 #H @(fsups_ind … H) -L2 -T2 [ /2 width=3/ ]
 #L #L2 #T #T2 #_ #HT2 #IHT1 #U2 #HTU2
 elim (fsupq_cpxs_trans … HTU2 … HT2) -T2 #T2 #HT2 #HTU2
@@ -77,6 +77,6 @@ lapply (fsups_trans … HT2 … HTU2) -L -T2 /2 width=3/
 qed-.
 
 lemma fsup_ssta_trans: ∀h,g,L1,L2,T1,T2. ⦃L1, T1⦄ ⊃ ⦃L2, T2⦄ →
-                       ∀U2,l. ⦃h, L2⦄ ⊢ T2 •[g] ⦃l+1, U2⦄ →
-                       ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[g] U1 & ⦃L1, U1⦄ ⊃⸮ ⦃L2, U2⦄.
+                       ∀U2,l. ⦃h, L2⦄ ⊢ T2 •[h, g] ⦃l+1, U2⦄ →
+                       ∃∃U1. ⦃h, L1⦄ ⊢ T1 ➡[h, g] U1 & ⦃L1, U1⦄ ⊃⸮ ⦃L2, U2⦄.
 /3 width=4 by fsup_cpx_trans, ssta_cpx/ qed-.