made executable again

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / relocation / drops_sex.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
index d9a9588a346a996138c2c8edcda6c6a8f9123284..3195ebd2195cbb9b14b27583ae668e366d9763f8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
@@ -26,19 +26,19 @@ lemma sex_co_dropable_sn (RN) (RP):
 [ #f #Hf #_ #f2 #X #H #f1 #Hf2 >(sex_inv_atom1 … H) -X
   /4 width=3 by sex_atom, drops_atom, ex2_intro/
 | #f #I1 #L1 #K1 #_ #IH #Hf #f2 #X #H #f1 #Hf2
-  elim (coafter_inv_nxx … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H2 destruct
+  elim (pr_coafter_inv_next_sn … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H2 destruct
   elim (sex_inv_push1 … H) -H #I2 #L2 #HL12 #HI12 #H destruct
   elim (IH … HL12 … Hg2) -g2
-  /3 width=3 by isuni_inv_next, drops_drop, ex2_intro/
+  /3 width=3 by pr_isu_inv_next, drops_drop, ex2_intro/
 | #f #I1 #J1 #L1 #K1 #HLK #HJI1 #IH #Hf #f2 #X #H #f1 #Hf2
-  lapply (isuni_inv_push … Hf ??) -Hf [3: |*: // ] #Hf
+  lapply (pr_isu_inv_push … Hf ??) -Hf [3: |*: // ] #Hf
   lapply (drops_fwd_isid … HLK … Hf) -HLK #H0 destruct
   lapply (liftsb_fwd_isid … HJI1 … Hf) -HJI1 #H0 destruct
-  elim (coafter_inv_pxx … Hf2) -Hf2 [1,3:* |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
+  elim (pr_coafter_inv_push_sn … Hf2) -Hf2 [1,3:* |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
   [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #I2 #L2 #HL12 #HI12 #H destruct
-  elim (IH … HL12 … Hg2) -g2 -IH /2 width=1 by isuni_isid/ #K2 #HK12 #HLK2
+  elim (IH … HL12 … Hg2) -g2 -IH /2 width=1 by pr_isu_isi/ #K2 #HK12 #HLK2
   lapply (drops_fwd_isid … HLK2 … Hf) -HLK2 #H0 destruct
-  /4 width=3 by drops_refl, sex_next, sex_push, isid_push, ex2_intro/
+  /4 width=3 by drops_refl, sex_next, sex_push, pr_isi_push, ex2_intro/
 ]
 qed-.
 
@@ -49,13 +49,13 @@ lemma sex_liftable_co_dedropable_bi (RN) (RP):
       f ~⊚ f1 ≘ f2 → L1 ⪤[RN,RP,f2] L2.
 #RN #RP #HRN #HRP #f2 #L1 #L2 #H elim H -f2 -L1 -L2 //
 #g2 #I1 #I2 #L1 #L2 #HL12 #HI12 #IH #f1 #Y1 #Y2 #HK12 #b #f #HY1 #HY2 #H
-[ elim (coafter_inv_xxn … H) [ |*: // ] -H #g #g1 #Hg2 #H1 #H2 destruct
+[ elim (pr_coafter_inv_next … H) [ |*: // ] -H #g #g1 #Hg2 #H1 #H2 destruct
   elim (drops_inv_skip1 … HY1) -HY1 #J1 #K1 #HLK1 #HJI1 #H destruct
   elim (drops_inv_skip1 … HY2) -HY2 #J2 #K2 #HLK2 #HJI2 #H destruct
   elim (sex_inv_next … HK12) -HK12 #HK12 #HJ12
   elim (HRN … HJ12 … HLK1 … HJI1) -HJ12 -HJI1 #Z #Hz
   >(liftsb_mono … Hz … HJI2) -Z /3 width=9 by sex_next/
-| elim (coafter_inv_xxp … H) [1,2: |*: // ] -H *
+| elim (pr_coafter_inv_push … H) [1,2: |*: // ] -H *
   [ #g #g1 #Hg2 #H1 #H2 destruct
     elim (drops_inv_skip1 … HY1) -HY1 #J1 #K1 #HLK1 #HJI1 #H destruct
     elim (drops_inv_skip1 … HY2) -HY2 #J2 #K2 #HLK2 #HJI2 #H destruct
@@ -78,11 +78,11 @@ lemma sex_liftable_co_dedropable_sn (RN) (RP):
 [ #f #Hf #X #f1 #H #f2 #Hf2 >(sex_inv_atom1 … H) -X
   /4 width=4 by drops_atom, sex_atom, ex3_intro/
 | #f #I1 #L1 #K1 #_ #IHLK1 #K2 #f1 #HK12 #f2 #Hf2
-  elim (coafter_inv_nxx … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
+  elim (pr_coafter_inv_next_sn … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
   elim (IHLK1 … HK12 … Hg2) -K1
   /3 width=6 by drops_drop, sex_next, sex_push, ex3_intro/
 | #f #I1 #J1 #L1 #K1 #HLK1 #HJI1 #IHLK1 #X #f1 #H #f2 #Hf2
-  elim (coafter_inv_pxx … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
+  elim (pr_coafter_inv_push_sn … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
   [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #J2 #K2 #HK12 #HJ12 #H destruct
   [ elim (H2RP … HJ12 … HLK1 … HJI1) | elim (H2RN … HJ12 … HLK1 … HJI1) ] -J1
   elim (IHLK1 … HK12 … Hg2) -K1
@@ -91,25 +91,25 @@ lemma sex_liftable_co_dedropable_sn (RN) (RP):
 qed-.
 
 fact sex_dropable_dx_aux (RN) (RP):
-     â\88\80b,f,L2,K2. â\87©*[b,f] L2 â\89\98 K2 â\86\92 ð\9d\90\94â\9dªfâ\9d« →
+     â\88\80b,f,L2,K2. â\87©*[b,f] L2 â\89\98 K2 â\86\92 ð\9d\90\94â\9d¨fâ\9d© →
      ∀f2,L1. L1 ⪤[RN,RP,f2] L2 → ∀f1. f ~⊚ f1 ≘ f2 →
      ∃∃K1. ⇩*[b,f] L1 ≘ K1 & K1 ⪤[RN,RP,f1] K2.
 #RN #RP #b #f #L2 #K2 #H elim H -f -L2 -K2
 [ #f #Hf #_ #f2 #X #H #f1 #Hf2 lapply (sex_inv_atom2 … H) -H
   #H destruct /4 width=3 by sex_atom, drops_atom, ex2_intro/
 | #f #I2 #L2 #K2 #_ #IH #Hf #f2 #X #HX #f1 #Hf2
-  elim (coafter_inv_nxx … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
+  elim (pr_coafter_inv_next_sn … Hf2) -Hf2 [2,3: // ] #g2 #Hg2 #H destruct
   elim (sex_inv_push2 … HX) -HX #I1 #L1 #HL12 #HI12 #H destruct
   elim (IH … HL12 … Hg2) -L2 -I2 -g2
-  /3 width=3 by drops_drop, isuni_inv_next, ex2_intro/
+  /3 width=3 by drops_drop, pr_isu_inv_next, ex2_intro/
 | #f #I2 #J2 #L2 #K2 #_ #HJI2 #IH #Hf #f2 #X #HX #f1 #Hf2
-  elim (coafter_inv_pxx … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
+  elim (pr_coafter_inv_push_sn … Hf2) -Hf2 [1,3: * |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
   [ elim (sex_inv_push2 … HX) | elim (sex_inv_next2 … HX) ] -HX #I1 #L1 #HL12 #HI12 #H destruct
-  elim (IH … HL12 … Hg2) -L2 -g2 /2 width=3 by isuni_fwd_push/ #K1 #HLK1 #HK12
-  lapply (isuni_inv_push … Hf ??) -Hf [3,6: |*: // ] #Hf
+  elim (IH … HL12 … Hg2) -L2 -g2 /2 width=3 by pr_isu_fwd_push/ #K1 #HLK1 #HK12
+  lapply (pr_isu_inv_push … Hf ??) -Hf [3,6: |*: // ] #Hf
   lapply (liftsb_fwd_isid … HJI2 … Hf) #H destruct -HJI2
   lapply (drops_fwd_isid … HLK1 … Hf) #H destruct -HLK1
-  /4 width=5 by sex_next, sex_push, drops_refl, isid_push, ex2_intro/
+  /4 width=5 by sex_next, sex_push, drops_refl, pr_isi_push, ex2_intro/
 ]
 qed-.
 
@@ -119,7 +119,7 @@ lemma sex_co_dropable_dx (RN) (RP):
 
 lemma sex_drops_conf_next (RN) (RP):
       ∀f2,L1,L2. L1 ⪤[RN,RP,f2] L2 →
-      â\88\80b,f,I1,K1. â\87©*[b,f] L1 â\89\98 K1.â\93\98[I1] â\86\92 ð\9d\90\94â\9dªfâ\9d« →
+      â\88\80b,f,I1,K1. â\87©*[b,f] L1 â\89\98 K1.â\93\98[I1] â\86\92 ð\9d\90\94â\9d¨fâ\9d© →
       ∀f1. f ~⊚ ↑f1 ≘ f2 →
       ∃∃I2,K2. ⇩*[b,f] L2 ≘ K2.ⓘ[I2] & K1 ⪤[RN,RP,f1] K2 & RN K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
@@ -130,7 +130,7 @@ qed-.
 
 lemma sex_drops_conf_push (RN) (RP):
       ∀f2,L1,L2. L1 ⪤[RN,RP,f2] L2 →
-      â\88\80b,f,I1,K1. â\87©*[b,f] L1 â\89\98 K1.â\93\98[I1] â\86\92 ð\9d\90\94â\9dªfâ\9d« →
+      â\88\80b,f,I1,K1. â\87©*[b,f] L1 â\89\98 K1.â\93\98[I1] â\86\92 ð\9d\90\94â\9d¨fâ\9d© →
       ∀f1. f ~⊚ ⫯f1 ≘ f2 →
       ∃∃I2,K2. ⇩*[b,f] L2 ≘ K2.ⓘ[I2] & K1 ⪤[RN,RP,f1] K2 & RP K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
@@ -141,7 +141,7 @@ qed-.
 
 lemma sex_drops_trans_next (RN) (RP):
       ∀f2,L1,L2. L1 ⪤[RN,RP,f2] L2 →
-      â\88\80b,f,I2,K2. â\87©*[b,f] L2 â\89\98 K2.â\93\98[I2] â\86\92 ð\9d\90\94â\9dªfâ\9d« →
+      â\88\80b,f,I2,K2. â\87©*[b,f] L2 â\89\98 K2.â\93\98[I2] â\86\92 ð\9d\90\94â\9d¨fâ\9d© →
       ∀f1. f ~⊚ ↑f1 ≘ f2 →
       ∃∃I1,K1. ⇩*[b,f] L1 ≘ K1.ⓘ[I1] & K1 ⪤[RN,RP,f1] K2 & RN K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
@@ -151,7 +151,7 @@ elim (sex_co_dropable_dx … HL12 … HLK2 … Hf … Hf2) -L2 -f2 -Hf
 qed-.
 
 lemma sex_drops_trans_push (RN) (RP): ∀f2,L1,L2. L1 ⪤[RN,RP,f2] L2 →
-      â\88\80b,f,I2,K2. â\87©*[b,f] L2 â\89\98 K2.â\93\98[I2] â\86\92 ð\9d\90\94â\9dªfâ\9d« →
+      â\88\80b,f,I2,K2. â\87©*[b,f] L2 â\89\98 K2.â\93\98[I2] â\86\92 ð\9d\90\94â\9d¨fâ\9d© →
       ∀f1. f ~⊚ ⫯f1 ≘ f2 →
       ∃∃I1,K1. ⇩*[b,f] L1 ≘ K1.ⓘ[I1] & K1 ⪤[RN,RP,f1] K2 & RP K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
@@ -187,7 +187,7 @@ elim (sex_liftable_co_dedropable_sn … H1RN H1RP H2RN H2RP … HLK1 … HK12 
 qed-.
 
 lemma drops_atom2_sex_conf (RN) (RP):
-      â\88\80b,f1,L1. â\87©*[b,f1] L1 â\89\98 â\8b\86 â\86\92 ð\9d\90\94â\9dªf1â\9d« →
+      â\88\80b,f1,L1. â\87©*[b,f1] L1 â\89\98 â\8b\86 â\86\92 ð\9d\90\94â\9d¨f1â\9d© →
       ∀f,L2. L1 ⪤[RN,RP,f] L2 →
       ∀f2. f1 ~⊚ f2 ≘f → ⇩*[b,f1] L2 ≘ ⋆.
 #RN #RP #b #f1 #L1 #H1 #Hf1 #f #L2 #H2 #f2 #H3
@@ -198,23 +198,23 @@ qed-.
 lemma sex_sdj_split_dx (R1) (R2) (RP):
       c_reflexive … R1 → c_reflexive … R2 → c_reflexive … RP →
       ∀L1,f1.
-      (â\88\80g,I,K,n. â\87©[n] L1 â\89\98 K.â\93\98[I] â\86\92 â\86\91g = ⫱*[n] f1 → R_pw_confluent1_sex R1 R1 R2 cfull g K I) →
+      (â\88\80g,I,K,n. â\87©[n] L1 â\89\98 K.â\93\98[I] â\86\92 â\86\91g = â«°*[n] f1 → R_pw_confluent1_sex R1 R1 R2 cfull g K I) →
       ∀L2. L1 ⪤[R1,RP,f1] L2 → ∀f2. f1 ∥ f2 →
       ∃∃L. L1 ⪤[R2,cfull,f1] L & L ⪤[RP,R1,f2] L2.
 #R1 #R2 #RP #HR1 #HR2 #HRP #L1 elim L1 -L1
 [ #f1 #_ #L2 #H #f2 #_
   lapply (sex_inv_atom1 … H) -H #H destruct
   /2 width=3 by sex_atom, ex2_intro/
-| #K1 #I1 #IH #f1 elim (pn_split f1) * #g1 #H destruct
+| #K1 #I1 #IH #f1 elim (pr_map_split_tl f1) * #g1 #H destruct
   #HR #L2 #H #f2 #Hf
   [ elim (sex_inv_push1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct
-    elim (sdj_inv_px … Hf ??) -Hf [1,3: * |*: // ] #g2 #Hg #H destruct
+    elim (pr_sdj_inv_push_sn … Hf ??) -Hf [1,3: * |*: // ] #g2 #Hg #H destruct
     elim (IH … HK12 … Hg) -IH -HK12 -Hg
     [1,3: /3 width=5 by sex_next, sex_push, ex2_intro/
     |2,4: /3 width=3 by drops_drop/
     ]
   | elim (sex_inv_next1 … H) -H #I2 #K2 #HK12 #HI12 #H destruct
-    elim (sdj_inv_nx … Hf ??) -Hf [|*: // ] #g2 #Hg #H destruct
+    elim (pr_sdj_inv_next_sn … Hf ??) -Hf [|*: // ] #g2 #Hg #H destruct
     elim (IH … HK12 … Hg) -IH -HK12 -Hg
     [ /5 width=11 by sex_next, sex_push, drops_refl, ex2_intro/
     | /3 width=3 by drops_drop/