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

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma
index e57f37d9da00f3e886f832a0fbe8c258602a16d0..7a4513fb9b98893ebdf6bcec3eb0da903a95a0d8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma
@@ -21,8 +21,8 @@ include "basic_2/computation/csn.ma".
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was just: sn3_lift *)
-lemma csn_lift: ∀h,g,L2,L1,T1,d,e. ⦃h, L1⦄ ⊢ ⬊*[g] T1 →
-                ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → ⦃h, L2⦄ ⊢ ⬊*[g] T2.
+lemma csn_lift: ∀h,g,L2,L1,T1,d,e. ⦃h, L1⦄ ⊢ ⬊*[h, g] T1 →
+                ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → ⦃h, L2⦄ ⊢ ⬊*[h, g] T2.
 #h #g #L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL21 #HT12
 @csn_intro #T #HLT2 #HT2
 elim (cpx_inv_lift1 … HLT2 … HL21 … HT12) -HLT2 #T0 #HT0 #HLT10
@@ -31,8 +31,8 @@ elim (cpx_inv_lift1 … HLT2 … HL21 … HT12) -HLT2 #T0 #HT0 #HLT10
 qed.
 
 (* Basic_1: was just: sn3_gen_lift *)
-lemma csn_inv_lift: ∀h,g,L2,L1,T1,d,e. ⦃h, L1⦄ ⊢ ⬊*[g] T1 →
-                    ∀T2. ⇩[d, e] L1 ≡ L2 → ⇧[d, e] T2 ≡ T1 → ⦃h, L2⦄ ⊢ ⬊*[g] T2.
+lemma csn_inv_lift: ∀h,g,L2,L1,T1,d,e. ⦃h, L1⦄ ⊢ ⬊*[h, g] T1 →
+                    ∀T2. ⇩[d, e] L1 ≡ L2 → ⇧[d, e] T2 ≡ T1 → ⦃h, L2⦄ ⊢ ⬊*[h, g] T2.
 #h #g #L2 #L1 #T1 #d #e #H elim H -T1 #T1 #_ #IHT1 #T2 #HL12 #HT21
 @csn_intro #T #HLT2 #HT2
 elim (lift_total T d e) #T0 #HT0
@@ -44,7 +44,7 @@ qed.
 (* Advanced properties ******************************************************)
 
 (* Basic_1: was just: sn3_abbr *)
-lemma csn_lref_bind: ∀h,g,I,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃h, K⦄ ⊢ ⬊*[g] V → ⦃h, L⦄ ⊢ ⬊*[g] #i.
+lemma csn_lref_bind: ∀h,g,I,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃h, K⦄ ⊢ ⬊*[h, g] V → ⦃G, L⦄ ⊢ ⬊*[h, g] #i.
 #h #g #I #L #K #V #i #HLK #HV
 @csn_intro #X #H #Hi
 elim (cpx_inv_lref1 … H) -H
@@ -57,9 +57,9 @@ elim (cpx_inv_lref1 … H) -H
 ]
 qed.
 
-lemma csn_appl_simple: ∀h,g,L,V. ⦃h, L⦄ ⊢ ⬊*[g] V → ∀T1.
-                       (∀T2. ⦃h, L⦄ ⊢ T1 ➡[g] T2 → (T1 = T2 → ⊥) → ⦃h, L⦄ ⊢ ⬊*[g] ⓐV.T2) →
-                       𝐒⦃T1⦄ → ⦃h, L⦄ ⊢ ⬊*[g] ⓐV.T1.
+lemma csn_appl_simple: ∀h,g,L,V. ⦃G, L⦄ ⊢ ⬊*[h, g] V → ∀T1.
+                       (∀T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 → (T1 = T2 → ⊥) → ⦃G, L⦄ ⊢ ⬊*[h, g] ⓐV.T2) →
+                       𝐒⦃T1⦄ → ⦃G, L⦄ ⊢ ⬊*[h, g] ⓐV.T1.
 #h #g #L #V #H @(csn_ind … H) -V #V #_ #IHV #T1 #IHT1 #HT1
 @csn_intro #X #H1 #H2
 elim (cpx_inv_appl1_simple … H1) // -H1
@@ -80,7 +80,7 @@ qed.
 
 (* Basic_1: was: sn3_gen_def *)
 lemma csn_inv_lref_bind: ∀h,g,I,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V →
-                         ⦃h, L⦄ ⊢ ⬊*[g] #i → ⦃h, K⦄ ⊢ ⬊*[g] V.
+                         ⦃G, L⦄ ⊢ ⬊*[h, g] #i → ⦃h, K⦄ ⊢ ⬊*[h, g] V.
 #h #g #I #L #K #V #i #HLK #Hi
 elim (lift_total V 0 (i+1)) #V0 #HV0
 lapply (ldrop_fwd_ldrop2 … HLK) #H0LK