X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Fgcp_cr.ma;h=f9b13438a48d90c658093c8a181de7ccc1b43841;hp=09dd1d346e6ada868061291c8880a26f8d2c8647;hb=222044da28742b24584549ba86b1805a87def070;hpb=38571b4c3881f2b59b7a2cdd016c83b161d3d755

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/gcp_cr.ma b/matita/matita/contribs/lambdadelta/basic_2/static/gcp_cr.ma
index 09dd1d346..f9b13438a 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/gcp_cr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/gcp_cr.ma
@@ -39,11 +39,11 @@ definition S4 ≝ λRP,C:candidate.
                 ∀G,L,Vs. all … (RP G L) Vs → ∀s. C G L (ⒶVs.⋆s).
 
 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.
@@ -63,7 +63,7 @@ record gcr (RR:relation4 genv lenv term term) (RS:relation term) (RP,C:candidate
 (* the functional construction for candidates *)
 definition cfun: candidate → candidate → candidate ≝
                  λC1,C2,G,K,T. ∀f,L,W,U.
-                 ⬇*[Ⓕ, f] L ≡ K → ⬆*[f] T ≡ U → C1 G L W → C2 G L (ⓐW.U).
+                 ⬇*[Ⓕ, f] L ≘ K → ⬆*[f] T ≘ U → C1 G L W → C2 G L (ⓐW.U).
 
 (* the reducibility candidate associated to an atomic arity *)
 rec definition acr (RP:candidate) (A:aarity) on A: candidate ≝
@@ -105,57 +105,58 @@ lemma acr_gcr: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP →
 #B #A #IHB #IHA @mk_gcr
 [ #G #L #T #H
   elim (cp1 … H1RP G L) #s #HK
-  lapply (s2 … IHB G L (◊) … HK) // #HB
+  lapply (s2 … IHB G L (Ⓔ) … HK) // #HB
   lapply (H (𝐈𝐝) 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
   lapply (s1 … IHB … HB) #HV0
-  @(s2 … IHA  … (V0@V0s)) /3 width=13 by cp0, gcp2_all, lifts_simple_dx, conj/
+  @(s2 … IHA  … (V0⨮V0s)) /3 width=13 by cp0, gcp2_all, lifts_simple_dx, conj/
 | #p #G #L #Vs #U #T #W #HA #f #L0 #V0 #X #HL0 #H #HB
-  elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
-  elim (lifts_inv_flat1 … HY) -HY #U0 #X #HU0 #HX #H destruct
+  elim (lifts_inv_applv1 … H) -H #V0s #X0 #HV0s #H0 #H destruct
+  elim (lifts_inv_flat1 … H0) -H0 #U0 #X #HU0 #HX #H destruct
   elim (lifts_inv_bind1 … HX) -HX #W0 #T0 #HW0 #HT0 #H destruct
-  @(s3 … IHA … (V0@V0s)) /5 width=6 by lifts_applv, lifts_flat, lifts_bind/
+  @(s3 … IHA … (V0⨮V0s)) /5 width=6 by lifts_applv, lifts_flat, lifts_bind/
 | #G #L #Vs #HVs #s #f #L0 #V0 #X #HL0 #H #HB
-  elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
-  >(lifts_inv_sort1 … HY) -Y
+  elim (lifts_inv_applv1 … H) -H #V0s #X0 #HV0s #H0 #H destruct
+  >(lifts_inv_sort1 … H0) -X0
   lapply (s1 … IHB … HB) #HV0
-  @(s4 … IHA … (V0@V0s)) /3 width=7 by gcp2_all, conj/
+  @(s4 … IHA … (V0⨮V0s)) /3 width=7 by gcp2_all, conj/
 | #I #G #L #K #Vs #V1 #V2 #i #HA #HV12 #HLK #f #L0 #V0 #X #HL0 #H #HB
-  elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
-  elim (lifts_inv_lref1 … HY) -HY #j #Hf #H destruct
+  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
   lapply (drops_tls_at … Hf … HY) -HY #HY
-  elim (drops_inv_skip2 … HY) -HY #K0 #W1 #_ #HVW1 #H destruct
-  elim (lifts_total W1 (𝐔❴⫯j❵)) #W2 #HW12
+  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
-  @(s5 … IHA … (V0@V0s) … HW12) /3 width=4 by drops_inv_gen, lifts_applv/
+  @(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 #Y #HV10s #HY #H destruct
-  elim (lifts_inv_bind1 … HY) -HY #V0 #T0 #HV0 #HT0 #H destruct
+  elim (lifts_inv_applv1 … H) -H #V10s #X0 #HV10s #H0 #H destruct
+  elim (lifts_inv_bind1 … H0) -H0 #V0 #T0 #HV0 #HT0 #H destruct
   elim (lifts_total V10 (𝐔❴1❵)) #V20 #HV120
   elim (liftsv_total (𝐔❴1❵) V10s) #V20s #HV120s
-  @(s6 … IHA … (V10@V10s) (V20@V20s)) /3 width=7 by cp2, liftsv_cons/
-  @(HA … (↑f)) /2 width=2 by drops_skip/
+  @(s6 … IHA … (V10⨮V10s) (V20⨮V20s)) /3 width=7 by cp2, liftsv_cons/
+  @(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 after_uni_one_sn/ #V10s #HV10s #HV120s
     >(liftsv_mono … HV12s … HV10s) -V1s //
   | @(acr_lifts … H1RP … HB … HV120) /3 width=2 by drops_refl, drops_drop/
   ]
 | #G #L #Vs #T #W #HA #HW #f #L0 #V0 #X #HL0 #H #HB
-  elim (lifts_inv_applv1 … H) -H #V0s #Y #HV0s #HY #H destruct
-  elim (lifts_inv_flat1 … HY) -HY #W0 #T0 #HW0 #HT0 #H destruct
-  @(s7 … IHA … (V0@V0s)) /3 width=5 by lifts_applv/
+  elim (lifts_inv_applv1 … H) -H #V0s #X0 #HV0s #H0 #H destruct
+  elim (lifts_inv_flat1 … H0) -H0 #W0 #T0 #HW0 #HT0 #H destruct
+  @(s7 … IHA … (V0⨮V0s)) /3 width=5 by lifts_applv/
 ]
 qed.
 
 lemma acr_abst: ∀RR,RS,RP. gcp RR RS RP → gcr RR RS RP RP →
                 ∀p,G,L,W,T,A,B. ⦃G, L, W⦄ ϵ[RP] 〚B〛 → (
-                   ∀b,f,L0,V0,W0,T0. ⬇*[b, f] L0 ≡ L → ⬆*[f] W ≡ W0 → ⬆*[↑f] T ≡ T0 →
+                   ∀b,f,L0,V0,W0,T0. ⬇*[b, f] L0 ≘ L → ⬆*[f] W ≘ W0 → ⬆*[⫯f] T ≘ T0 →
                                    ⦃G, L0, V0⦄ ϵ[RP] 〚B〛 → ⦃G, L0, W0⦄ ϵ[RP] 〚B〛 → ⦃G, L0.ⓓⓝW0.V0, T0⦄ ϵ[RP] 〚A〛
                 ) →
                 ⦃G, L, ⓛ{p}W.T⦄ ϵ[RP] 〚②B.A〛.
@@ -164,11 +165,11 @@ lapply (acr_gcr … H1RP H2RP A) #HCA
 lapply (acr_gcr … H1RP H2RP B) #HCB
 elim (lifts_inv_bind1 … H) -H #W0 #T0 #HW0 #HT0 #H destruct
 lapply (acr_lifts … H1RP … HW … HL0 … HW0) -HW #HW0
-lapply (s3 … HCA … p G L0 (◊)) #H @H -H
-lapply (s6 … HCA G L0 (◊) (◊) ?) // #H @H -H
+lapply (s3 … HCA … p G L0 (Ⓔ)) #H @H -H
+lapply (s6 … HCA G L0 (Ⓔ) (Ⓔ) ?) // #H @H -H
 [ @(HA … HL0) //
 | lapply (s1 … HCB) -HCB #HCB
-  lapply (s7 … H2RP G L0 (◊)) /3 width=1 by/
+  lapply (s7 … H2RP G L0 (Ⓔ)) /3 width=1 by/
 ]
 qed.