partial commit: "computation" component ...

[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 7a4513fb9b98893ebdf6bcec3eb0da903a95a0d8..5658ab3643f4a8bc5423f55c0962bf84a2f7b13d 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/csn_lift.ma
@@ -12,18 +12,18 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "basic_2/computation/csn.ma". (**) (* disambiguation error *)
 include "basic_2/reduction/cnx_lift.ma".
 include "basic_2/computation/acp.ma".
-include "basic_2/computation/csn.ma".
 
 (* CONTEXT-SENSITIVE EXTENDED STRONGLY NORMALIZING TERMS ********************)
 
 (* Relocation properties ****************************************************)
 
 (* Basic_1: was just: sn3_lift *)
-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
+lemma csn_lift: ∀h,g,G,L2,L1,T1,d,e. ⦃G, L1⦄ ⊢ ⬊*[h, g] T1 →
+                ∀T2. ⇩[d, e] L2 ≡ L1 → ⇧[d, e] T1 ≡ T2 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
+#h #g #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
 @(IHT1 … HLT10) // -L1 -L2 #H destruct
@@ -31,9 +31,9 @@ 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⦄ ⊢ ⬊*[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
+lemma csn_inv_lift: ∀h,g,G,L2,L1,T1,d,e. ⦃G, L1⦄ ⊢ ⬊*[h, g] T1 →
+                    ∀T2. ⇩[d, e] L1 ≡ L2 → ⇧[d, e] T2 ≡ T1 → ⦃G, L2⦄ ⊢ ⬊*[h, g] T2.
+#h #g #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
 lapply (cpx_lift … HLT2 … HL12 … HT21 … HT0) -HLT2 #HLT10
@@ -44,8 +44,8 @@ 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⦄ ⊢ ⬊*[h, g] V → ⦃G, L⦄ ⊢ ⬊*[h, g] #i.
-#h #g #I #L #K #V #i #HLK #HV
+lemma csn_lref_bind: ∀h,g,I,G,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ ⬊*[h, g] V → ⦃G, L⦄ ⊢ ⬊*[h, g] #i.
+#h #g #I #G #L #K #V #i #HLK #HV
 @csn_intro #X #H #Hi
 elim (cpx_inv_lref1 … H) -H
 [ #H destruct elim Hi //
@@ -57,10 +57,10 @@ elim (cpx_inv_lref1 … H) -H
 ]
 qed.
 
-lemma csn_appl_simple: ∀h,g,L,V. ⦃G, L⦄ ⊢ ⬊*[h, g] V → ∀T1.
+lemma csn_appl_simple: ∀h,g,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
+#h #g #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
 #V0 #T0 #HLV0 #HLT10 #H destruct
@@ -79,9 +79,9 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_1: was: sn3_gen_def *)
-lemma csn_inv_lref_bind: ∀h,g,I,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V →
-                         ⦃G, L⦄ ⊢ ⬊*[h, g] #i → ⦃h, K⦄ ⊢ ⬊*[h, g] V.
-#h #g #I #L #K #V #i #HLK #Hi
+lemma csn_inv_lref_bind: ∀h,g,I,G,L,K,V,i. ⇩[0, i] L ≡ K.ⓑ{I}V →
+                         ⦃G, L⦄ ⊢ ⬊*[h, g] #i → ⦃G, K⦄ ⊢ ⬊*[h, g] V.
+#h #g #I #G #L #K #V #i #HLK #Hi
 elim (lift_total V 0 (i+1)) #V0 #HV0
 lapply (ldrop_fwd_ldrop2 … HLK) #H0LK
 @(csn_inv_lift … H0LK … HV0) -H0LK
@@ -92,7 +92,7 @@ qed-.
 
 theorem csn_acp: ∀h,g. acp (cpx h g) (eq …) (csn h g).
 #h #g @mk_acp
-[ #L elim (deg_total h g 0)
+[ #G #L elim (deg_total h g 0)
   #l #Hl lapply (cnx_sort_iter … L … Hl) /2 width=2/
 | @cnx_lift
 | /2 width=3 by csn_fwd_flat_dx/