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 129f950eb5cbf44dd036cf191775eb7c2e2689d1..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
@@ -87,7 +87,7 @@ 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 →
                           ∃∃K1. ⇩*[b,f] L1 ≘ K1 & K1 ⪤[RN,RP,f1] K2.
 #RN #RP #b #f #L2 #K2 #H elim H -f -L2 -K2
@@ -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 →
-                           ∀b,f,I1,K1. ⇩*[b,f] L1 ≘ K1.ⓘ{I1} → 𝐔⦃f⦄ →
+                           ∀b,f,I1,K1. ⇩*[b,f] L1 ≘ K1.ⓘ[I1] → 𝐔❪f❫ →
                            ∀f1. f ~⊚ ↑f1 ≘ f2 →
-                           ∃∃I2,K2. ⇩*[b,f] L2 ≘ K2.ⓘ{I2} & K1 ⪤[RN,RP,f1] K2 & RN K1 I1 I2.
+                           ∃∃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
 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 →
-                           ∀b,f,I1,K1. ⇩*[b,f] L1 ≘ K1.ⓘ{I1} → 𝐔⦃f⦄ →
+                           ∀b,f,I1,K1. ⇩*[b,f] L1 ≘ K1.ⓘ[I1] → 𝐔❪f❫ →
                            ∀f1. f ~⊚ ⫯f1 ≘ f2 →
-                           ∃∃I2,K2. ⇩*[b,f] L2 ≘ K2.ⓘ{I2} & K1 ⪤[RN,RP,f1] K2 & RP K1 I1 I2.
+                           ∃∃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
 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 →
-                            ∀b,f,I2,K2. ⇩*[b,f] L2 ≘ K2.ⓘ{I2} → 𝐔⦃f⦄ →
+                            ∀b,f,I2,K2. ⇩*[b,f] L2 ≘ K2.ⓘ[I2] → 𝐔❪f❫ →
                             ∀f1. f ~⊚ ↑f1 ≘ f2 →
-                            ∃∃I1,K1. ⇩*[b,f] L1 ≘ K1.ⓘ{I1} & K1 ⪤[RN,RP,f1] K2 & RN K1 I1 I2.
+                            ∃∃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
 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 →
-                            ∀b,f,I2,K2. ⇩*[b,f] L2 ≘ K2.ⓘ{I2} → 𝐔⦃f⦄ →
+                            ∀b,f,I2,K2. ⇩*[b,f] L2 ≘ K2.ⓘ[I2] → 𝐔❪f❫ →
                             ∀f1. f ~⊚ ⫯f1 ≘ f2 →
-                            ∃∃I1,K1. ⇩*[b,f] L1 ≘ K1.ⓘ{I1} & K1 ⪤[RN,RP,f1] K2 & RP K1 I1 I2.
+                            ∃∃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
 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 →
-                            ∀b,f,I1,L1. ⇩*[b,f] L1.ⓘ{I1} ≘ K1 →
+                            ∀b,f,I1,L1. ⇩*[b,f] L1.ⓘ[I1] ≘ K1 →
                             ∀f2. f ~⊚ f1 ≘ ↑f2 →
-                            ∃∃I2,L2. ⇩*[b,f] L2.ⓘ{I2} ≘ K2 & L1 ⪤[RN,RP,f2] L2 & RN L1 I1 I2 & L1.ⓘ{I1} ≡[f] L2.ⓘ{I2}.
+                            ∃∃I2,L2. ⇩*[b,f] L2.ⓘ[I2] ≘ K2 & L1 ⪤[RN,RP,f2] L2 & RN L1 I1 I2 & L1.ⓘ[I1] ≡[f] L2.ⓘ[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
@@ -169,16 +169,16 @@ 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 →
-                            ∀b,f,I1,L1. ⇩*[b,f] L1.ⓘ{I1} ≘ K1 →
+                            ∀b,f,I1,L1. ⇩*[b,f] L1.ⓘ[I1] ≘ K1 →
                             ∀f2. f ~⊚ f1 ≘ ⫯f2 →
-                            ∃∃I2,L2. ⇩*[b,f] L2.ⓘ{I2} ≘ K2 & L1 ⪤[RN,RP,f2] L2 & RP L1 I1 I2 & L1.ⓘ{I1} ≡[f] L2.ⓘ{I2}.
+                            ∃∃I2,L2. ⇩*[b,f] L2.ⓘ[I2] ≘ K2 & L1 ⪤[RN,RP,f2] L2 & RP L1 I1 I2 & L1.ⓘ[I1] ≡[f] L2.ⓘ[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 →
                             ∀f2. f1 ~⊚ f2 ≘f → ⇩*[b,f1] L2 ≘ ⋆.
 #RN #RP #b #f1 #L1 #H1 #Hf1 #f #L2 #H2 #f2 #H3