update in ground_2, static_2, basic_2, apps_2, alpha_1

[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 8f3058cb9c4df9e987ceae60568cab86a12e3d88..edec3dcc5f88841327da1a83856e5675629cfa05 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
@@ -34,7 +34,7 @@ lemma sex_co_dropable_sn: ∀RN,RP. co_dropable_sn (sex RN RP).
   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 (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #I2 #L2 #HL12 #HI12 #H 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
   lapply (drops_fwd_isid … HLK2 … Hf) -HLK2 #H0 destruct
   /4 width=3 by drops_refl, sex_next, sex_push, isid_push, ex2_intro/
@@ -43,7 +43,7 @@ qed-.
 
 lemma sex_liftable_co_dedropable_bi: ∀RN,RP. d_liftable2_sn … liftsb RN → d_liftable2_sn … liftsb RP →
                                      ∀f2,L1,L2. L1 ⪤[cfull,RP,f2] L2 → ∀f1,K1,K2. K1 ⪤[RN,RP,f1] K2 →
-                                     â\88\80b,f. â¬\87*[b,f] L1 â\89\98 K1 â\86\92 â¬\87*[b,f] L2 ≘ K2 →
+                                     â\88\80b,f. â\87©*[b,f] L1 â\89\98 K1 â\86\92 â\87©*[b,f] L2 ≘ K2 →
                                      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
@@ -87,9 +87,9 @@ lemma sex_liftable_co_dedropable_sn: ∀RN,RP. (∀L. reflexive … (RN L)) →
 ]
 qed-.
 
-fact sex_dropable_dx_aux: â\88\80RN,RP,b,f,L2,K2. â¬\87*[b,f] L2 â\89\98 K2 â\86\92 ð\9d\90\94â¦\83fâ¦\84 →
+fact sex_dropable_dx_aux: â\88\80RN,RP,b,f,L2,K2. â\87©*[b,f] L2 â\89\98 K2 â\86\92 ð\9d\90\94â\9dªfâ\9d« →
                           ∀f2,L1. L1 ⪤[RN,RP,f2] L2 → ∀f1. f ~⊚ f1 ≘ f2 →
-                          â\88\83â\88\83K1. â¬\87*[b,f] L1 ≘ K1 & K1 ⪤[RN,RP,f1] K2.
+                          â\88\83â\88\83K1. â\87©*[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/
@@ -114,9 +114,9 @@ lemma sex_co_dropable_dx: ∀RN,RP. co_dropable_dx (sex 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¦\83fâ¦\84 →
+                           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« →
                            ∀f1. f ~⊚ ↑f1 ≘ f2 →
-                           â\88\83â\88\83I2,K2. â¬\87*[b,f] L2 â\89\98 K2.â\93\98{I2} & K1 ⪤[RN,RP,f1] K2 & RN K1 I1 I2.
+                           â\88\83â\88\83I2,K2. â\87©*[b,f] L2 â\89\98 K2.â\93\98[I2] & K1 ⪤[RN,RP,f1] K2 & RN K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
 elim (sex_co_dropable_sn … HLK1 … Hf … HL12 … Hf2) -L1 -f2 -Hf
 #X #HX #HLK2 elim (sex_inv_next1 … HX) -HX
@@ -125,9 +125,9 @@ 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¦\83fâ¦\84 →
+                           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« →
                            ∀f1. f ~⊚ ⫯f1 ≘ f2 →
-                           â\88\83â\88\83I2,K2. â¬\87*[b,f] L2 â\89\98 K2.â\93\98{I2} & K1 ⪤[RN,RP,f1] K2 & RP K1 I1 I2.
+                           â\88\83â\88\83I2,K2. â\87©*[b,f] L2 â\89\98 K2.â\93\98[I2] & K1 ⪤[RN,RP,f1] K2 & RP K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I1 #K1 #HLK1 #Hf #f1 #Hf2
 elim (sex_co_dropable_sn … HLK1 … Hf … HL12 … Hf2) -L1 -f2 -Hf
 #X #HX #HLK2 elim (sex_inv_push1 … HX) -HX
@@ -135,9 +135,9 @@ elim (sex_co_dropable_sn … HLK1 … Hf … HL12 … Hf2) -L1 -f2 -Hf
 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¦\83fâ¦\84 →
+                            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« →
                             ∀f1. f ~⊚ ↑f1 ≘ f2 →
-                            â\88\83â\88\83I1,K1. â¬\87*[b,f] L1 â\89\98 K1.â\93\98{I1} & K1 ⪤[RN,RP,f1] K2 & RN K1 I1 I2.
+                            â\88\83â\88\83I1,K1. â\87©*[b,f] L1 â\89\98 K1.â\93\98[I1] & K1 ⪤[RN,RP,f1] K2 & RN K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
 elim (sex_co_dropable_dx … HL12 … HLK2 … Hf … Hf2) -L2 -f2 -Hf
 #X #HLK1 #HX elim (sex_inv_next2 … HX) -HX
@@ -145,9 +145,9 @@ 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¦\83fâ¦\84 →
+                            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« →
                             ∀f1. f ~⊚ ⫯f1 ≘ f2 →
-                            â\88\83â\88\83I1,K1. â¬\87*[b,f] L1 â\89\98 K1.â\93\98{I1} & K1 ⪤[RN,RP,f1] K2 & RP K1 I1 I2.
+                            â\88\83â\88\83I1,K1. â\87©*[b,f] L1 â\89\98 K1.â\93\98[I1] & K1 ⪤[RN,RP,f1] K2 & RP K1 I1 I2.
 #RN #RP #f2 #L1 #L2 #HL12 #b #f #I2 #K2 #HLK2 #Hf #f1 #Hf2
 elim (sex_co_dropable_dx … HL12 … HLK2 … Hf … Hf2) -L2 -f2 -Hf
 #X #HLK1 #HX elim (sex_inv_push2 … HX) -HX
@@ -157,9 +157,9 @@ qed-.
 lemma drops_sex_trans_next: ∀RN,RP. (∀L. reflexive ? (RN L)) → (∀L. reflexive ? (RP L)) →
                             d_liftable2_sn … liftsb RN → d_liftable2_sn … liftsb RP →
                             ∀f1,K1,K2. K1 ⪤[RN,RP,f1] K2 →
-                            â\88\80b,f,I1,L1. â¬\87*[b,f] L1.â\93\98{I1} ≘ K1 →
+                            â\88\80b,f,I1,L1. â\87©*[b,f] L1.â\93\98[I1] ≘ K1 →
                             ∀f2. f ~⊚ f1 ≘ ↑f2 →
-                            â\88\83â\88\83I2,L2. â¬\87*[b,f] L2.â\93\98{I2} â\89\98 K2 & L1 ⪤[RN,RP,f2] L2 & RN L1 I1 I2 & L1.â\93\98{I1} â\89¡[f] L2.â\93\98{I2}.
+                            â\88\83â\88\83I2,L2. â\87©*[b,f] L2.â\93\98[I2] â\89\98 K2 & L1 ⪤[RN,RP,f2] L2 & RN L1 I1 I2 & L1.â\93\98[I1] â\89¡[f] L2.â\93\98[I2].
 #RN #RP #H1RN #H1RP #H2RN #H2RP #f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
 elim (sex_liftable_co_dedropable_sn … H1RN H1RP H2RN H2RP … HLK1 … HK12 … Hf2) -K1 -f1 -H1RN -H1RP -H2RN -H2RP
 #X #HX #HLK2 #H1L12 elim (sex_inv_next1 … HX) -HX
@@ -169,18 +169,18 @@ qed-.
 lemma drops_sex_trans_push: ∀RN,RP. (∀L. reflexive ? (RN L)) → (∀L. reflexive ? (RP L)) →
                             d_liftable2_sn … liftsb RN → d_liftable2_sn … liftsb RP →
                             ∀f1,K1,K2. K1 ⪤[RN,RP,f1] K2 →
-                            â\88\80b,f,I1,L1. â¬\87*[b,f] L1.â\93\98{I1} ≘ K1 →
+                            â\88\80b,f,I1,L1. â\87©*[b,f] L1.â\93\98[I1] ≘ K1 →
                             ∀f2. f ~⊚ f1 ≘ ⫯f2 →
-                            â\88\83â\88\83I2,L2. â¬\87*[b,f] L2.â\93\98{I2} â\89\98 K2 & L1 ⪤[RN,RP,f2] L2 & RP L1 I1 I2 & L1.â\93\98{I1} â\89¡[f] L2.â\93\98{I2}.
+                            â\88\83â\88\83I2,L2. â\87©*[b,f] L2.â\93\98[I2] â\89\98 K2 & L1 ⪤[RN,RP,f2] L2 & RP L1 I1 I2 & L1.â\93\98[I1] â\89¡[f] L2.â\93\98[I2].
 #RN #RP #H1RN #H1RP #H2RN #H2RP #f1 #K1 #K2 #HK12 #b #f #I1 #L1 #HLK1 #f2 #Hf2
 elim (sex_liftable_co_dedropable_sn … H1RN H1RP H2RN H2RP … HLK1 … HK12 … Hf2) -K1 -f1 -H1RN -H1RP -H2RN -H2RP
 #X #HX #HLK2 #H1L12 elim (sex_inv_push1 … HX) -HX
 #I2 #L2 #H2L12 #HI12 #H destruct /2 width=6 by ex4_2_intro/
 qed-.
 
-lemma drops_atom2_sex_conf: â\88\80RN,RP,b,f1,L1. â¬\87*[b,f1] L1 â\89\98 â\8b\86 â\86\92 ð\9d\90\94â¦\83f1â¦\84 →
+lemma drops_atom2_sex_conf: â\88\80RN,RP,b,f1,L1. â\87©*[b,f1] L1 â\89\98 â\8b\86 â\86\92 ð\9d\90\94â\9dªf1â\9d« →
                             ∀f,L2. L1 ⪤[RN,RP,f] L2 →
-                            â\88\80f2. f1 ~â\8a\9a f2 â\89\98f â\86\92 â¬\87*[b,f1] L2 ≘ ⋆.
+                            â\88\80f2. f1 ~â\8a\9a f2 â\89\98f â\86\92 â\87©*[b,f1] L2 ≘ ⋆.
 #RN #RP #b #f1 #L1 #H1 #Hf1 #f #L2 #H2 #f2 #H3
 elim (sex_co_dropable_sn … H1 … H2 … H3) // -H1 -H2 -H3 -Hf1
 #L #H #HL2 lapply (sex_inv_atom1 … H) -H //