X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fstatic%2Fgcp_aaa.ma;h=31bcb5aa52aca5f2cef4823ce19fe38493728915;hp=21382ed90863122184cded762ef4adbbeb923a0f;hb=222044da28742b24584549ba86b1805a87def070;hpb=98fbba1b68d457807c73ebf70eb2a48696381da4

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/gcp_aaa.ma b/matita/matita/contribs/lambdadelta/basic_2/static/gcp_aaa.ma
index 21382ed90..31bcb5aa5 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/static/gcp_aaa.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/gcp_aaa.ma
@@ -22,8 +22,8 @@ include "basic_2/static/lsubc_drops.ma".
 (* Basic_1: was: sc3_arity_csubc *)
 theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
                              gcp RR RS RP → gcr RR RS RP RP →
-                             ∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀b,f,L0. ⬇*[b, f] L0 ≡ L1 →
-                             ∀T0. ⬆*[f] T ≡ T0 → ∀L2. G ⊢ L2 ⫃[RP] L0 →
+                             ∀G,L1,T,A. ⦃G, L1⦄ ⊢ T ⁝ A → ∀b,f,L0. ⬇*[b, f] L0 ≘ L1 →
+                             ∀T0. ⬆*[f] T ≘ T0 → ∀L2. G ⊢ L2 ⫃[RP] L0 →
                              ⦃G, L2, T0⦄ ϵ[RP] 〚A〛.
 #RR #RS #RP #H1RP #H2RP #G #L1 #T @(fqup_wf_ind_eq (Ⓣ) … G L1 T) -G -L1 -T
 #Z #Y #X #IH #G #L1 * [ * | * [ #p ] * ]
@@ -31,7 +31,7 @@ theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
   lapply (aaa_inv_sort … HA) -HA #H destruct
   >(lifts_inv_sort1 … H0) -H0
   lapply (acr_gcr … H1RP H2RP (⓪)) #HAtom
-  lapply (s4 … HAtom G L2 (◊)) /2 width=1 by/
+  lapply (s4 … HAtom G L2 (Ⓔ)) /2 width=1 by/
 | #i #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct
   elim (aaa_inv_lref_drops … HA) -HA #I #K1 #V1 #HLK1 #HKV1
   elim (lifts_inv_lref1 … H0) -H0 #j #Hf #H destruct
@@ -41,21 +41,21 @@ theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
   lapply (drops_tls_at … Hf … HY) -Hf -HY #HY
   elim (drops_inv_skip2 … HY) -HY #Z #K0 #HK01 #HZ #H destruct
   elim (liftsb_inv_pair_sn … HZ) -HZ #V0 #HV10 #H destruct
-  elim (lifts_total V0 (𝐔❴⫯j❵)) #V #HV0
+  elim (lifts_total V0 (𝐔❴↑j❵)) #V #HV0
   elim (lsubc_drops_trans_isuni … HL20 … HLK0) -HL20 -HLK0 // #Y #HLK2 #H
   elim (lsubc_inv_bind2 … H) -H *
   [ #K2 #HK20 #H destruct
     lapply (drops_isuni_fwd_drop2 … HLK2) // #HLK2b
-    lapply (s5 … HA ? G ? ? (◊) … HV0 ?) -HA
+    lapply (s5 … HA ? G ? ? (Ⓔ) … HV0 ?) -HA
     /4 width=11 by acr_lifts, fqup_lref, drops_inv_gen/
   | #K2 #V2 #W2 #B #HKV2 #HK2V0 #HKV0B #_ #H1 #H2 destruct -IH -HLK1
     lapply (drops_isuni_fwd_drop2 … HLK2) // #HLK2b
     lapply (aaa_lifts … HKV1 … HK01 … HV10) -HKV1 -HK01 -HV10 #HKV0A
     lapply (aaa_mono … HKV0B … HKV0A) #H destruct -HKV0B -HKV0A
-    elim (lifts_total V2 (𝐔❴⫯j❵)) #V3 #HV23
-    lapply (s5 … HA … G … (◊) … (ⓝW2.V2) (ⓝV.V3) ????)
+    elim (lifts_total V2 (𝐔❴↑j❵)) #V3 #HV23
+    lapply (s5 … HA … G … (Ⓔ) … (ⓝW2.V2) (ⓝV.V3) ????)
     [3: |*: /2 width=9 by drops_inv_gen, lifts_flat/ ] -HLK2
-    lapply (s7 … HA G L2 (◊)) -HA /3 width=7 by acr_lifts/
+    lapply (s7 … HA G L2 (Ⓔ)) -HA /3 width=7 by acr_lifts/
   ]
 | #l #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct -IH
   elim (aaa_inv_gref … HA)
@@ -65,7 +65,7 @@ theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
   lapply (acr_gcr … H1RP H2RP A) #HA
   lapply (acr_gcr … H1RP H2RP B) #HB
   lapply (s1 … HB) -HB #HB
-  lapply (s6 … HA G L2 (◊) (◊)) /5 width=10 by lsubc_bind, liftsv_nil, drops_skip, ext2_pair/
+  lapply (s6 … HA G L2 (Ⓔ) (Ⓔ)) /5 width=10 by lsubc_bind, liftsv_nil, drops_skip, ext2_pair/
 | #W #T #HG #HL #HT #Z0 #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct
   elim (aaa_inv_abst … HA) -HA #B #A #HW #HT #H destruct
   elim (lifts_inv_bind1 … H0) -H0 #W0 #T0 #HW0 #HT0 #H destruct
@@ -74,7 +74,7 @@ theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
   elim (drops_lsubc_trans … H1RP … HL32 … HL20) -L2 #L2 #HL32 #HL20
   lapply (aaa_lifts … HW … (f3∘f) L2 … W3 ?) -HW
   [4: |*: /2 width=8 by drops_trans, lifts_trans/ ] #HW3
-  @(IH … ((↑f3)∘↑f) … (L2. ⓛW3)) -IH
+  @(IH … ((⫯f3)∘⫯f) … (L2. ⓛW3)) -IH
   /4 width=12 by lsubc_beta, drops_trans, drops_skip, lifts_trans, ext2_pair/
 | #V #T #HG #HL #HT #A #HA #b #f #L0 #HL01 #X0 #H0 #L2 #HL20 destruct
   elim (aaa_inv_appl … HA) -HA #B #HV #HT
@@ -85,7 +85,7 @@ theorem acr_aaa_csubc_lifts: ∀RR,RS,RP.
   elim (aaa_inv_cast … HA) -HA #HW #HT
   elim (lifts_inv_flat1 … H0) -H0 #W0 #T0 #HW0 #HT0 #H destruct
   lapply (acr_gcr … H1RP H2RP A) #HA
-  lapply (s7 … HA G L2 (◊)) /3 width=10 by/
+  lapply (s7 … HA G L2 (Ⓔ)) /3 width=10 by/
 ]
 qed.