partial commit in static_2

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / gcp_cr.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/gcp_cr.ma b/matita/matita/contribs/lambdadelta/static_2/static/gcp_cr.ma
index a8b71ee8bc45a787ef8863fce3ff89b71d6a7c26..e1b88f5b682d1f8ce0689e7556e3cb31c4311c41 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/gcp_cr.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/gcp_cr.ma
@@ -30,17 +30,17 @@ definition S2 ≝ λRR:relation4 genv lenv term term. λRS:relation term. λRP,C
                 ∀G,L,Vs. all … (RP G L) Vs →
                 ∀T. 𝐒❪T❫ → nf RR RS G L T → C G L (ⒶVs.T).
 
-(* Note: this generalizes Tait's ii *)
+(* Note: this generalizes Tait's ii, or Girard's CR3 *)
 definition S3 ≝ λC:candidate.
                 ∀a,G,L,Vs,V,T,W.
                 C G L (ⒶVs.ⓓ[a]ⓝW.V.T) → C G L (ⒶVs.ⓐV.ⓛ[a]W.T).
 
 definition S5 ≝ λC:candidate. ∀I,G,L,K,Vs,V1,V2,i.
-                C G L (ⒶVs.V2) → ⇧*[↑i] V1 ≘ V2 →
-                ⇩*[i] L ≘ K.ⓑ[I]V1 → C G L (ⒶVs.#i).
+                C G L (ⒶVs.V2) → ⇧[↑i] V1 ≘ V2 →
+                ⇩[i] L ≘ K.ⓑ[I]V1 → C G L (ⒶVs.#i).
 
 definition S6 ≝ λRP,C:candidate.
-                ∀G,L,V1b,V2b. ⇧*[1] V1b ≘ V2b →
+                ∀G,L,V1b,V2b. ⇧[1] V1b ≘ V2b →
                 ∀a,V,T. C G (L.ⓓV) (ⒶV2b.T) → RP G L V → C G L (ⒶV1b.ⓓ[a]V.T).
 
 definition S7 ≝ λC:candidate.
@@ -104,7 +104,7 @@ lemma acr_gcr: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP →
   letin s ≝ 0 (* one sort must exist *)
   lapply (cp1 … H1RP G L s) #HK
   lapply (s2 … IHB G L (Ⓔ) … HK) // #HB
-  lapply (H (ð\9d\90\88ð\9d\90\9d) L (⋆s) T ? ? ?) -H
+  lapply (H (ð\9d\90¢) L (⋆s) T ? ? ?) -H
   /3 width=6 by s1, cp3, drops_refl, lifts_refl/
 | #G #L #Vs #HVs #T #H1T #H2T #f #L0 #V0 #X #HL0 #H #HB
   elim (lifts_inv_applv1 … H) -H #V0s #T0 #HV0s #HT0 #H destruct
@@ -119,13 +119,13 @@ lemma acr_gcr: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP →
   elim (lifts_inv_applv1 … H) -H #V0s #X0 #HV0s #H0 #H destruct
   elim (lifts_inv_lref1 … H0) -H0 #j #Hf #H destruct
   lapply (drops_trans … HL0 … HLK ??) [3: |*: // ] -HLK #H
-  elim (drops_split_trans … H) -H [ |*: /2 width=6 by after_uni_dx/ ] #Y #HLK0 #HY
+  elim (drops_split_trans … H) -H [ |*: /2 width=6 by pr_after_nat_uni/ ] #Y #HLK0 #HY
   lapply (drops_tls_at … Hf … HY) -HY #HY
   elim (drops_inv_skip2 … HY) -HY #Z #K0 #HK0 #HZ #H destruct
   elim (liftsb_inv_pair_sn … HZ) -HZ #W1 #HVW1 #H destruct
   elim (lifts_total W1 (𝐔❨↑j❩)) #W2 #HW12
   lapply (lifts_trans … HVW1 … HW12 ??) -HVW1 [3: |*: // ] #H
-  lapply (lifts_conf … HV12 … H f ?) -V1 [ /2 width=3 by after_uni_succ_sn/ ] #HVW2
+  lapply (lifts_conf … HV12 … H f ?) -V1 [ /2 width=3 by pr_pat_after_uni_tls/ ] #HVW2
   @(s5 … IHA … (V0⨮V0s) … HW12) /3 width=4 by drops_inv_gen, lifts_applv/
 | #G #L #V1s #V2s #HV12s #p #V #T #HA #HV #f #L0 #V10 #X #HL0 #H #HB
   elim (lifts_inv_applv1 … H) -H #V10s #X0 #HV10s #H0 #H destruct
@@ -136,7 +136,7 @@ lemma acr_gcr: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP →
   @(HA … (⫯f)) /3 width=2 by drops_skip, ext2_pair/
   [ @lifts_applv //
     lapply (liftsv_trans … HV10s … HV120s ??) -V10s [3: |*: // ] #H
-    elim (liftsv_split_trans … H (𝐔❨1❩) (⫯f)) /2 width=1 by after_uni_one_sn/ #V10s #HV10s #HV120s
+    elim (liftsv_split_trans … H (𝐔❨1❩) (⫯f)) /2 width=1 by pr_after_unit_sn/ #V10s #HV10s #HV120s
     >(liftsv_mono … HV12s … HV10s) -V1s //
   | @(acr_lifts … H1RP … HB … HV120) /3 width=2 by drops_refl, drops_drop/
   ]