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[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 e1263a2fdedff474d5cb837d06f621bce898bfa3..8f3058cb9c4df9e987ceae60568cab86a12e3d88 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
@@ -42,9 +42,9 @@ lemma sex_co_dropable_sn: ∀RN,RP. co_dropable_sn (sex RN RP).
 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 →
-                                     ∀b,f. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
-                                     f ~⊚ f1 ≘ f2 → L1 ⪤[RN, RP, f2] L2.
+                                     ∀f2,L1,L2. L1 ⪤[cfull,RP,f2] L2 → ∀f1,K1,K2. K1 ⪤[RN,RP,f1] K2 →
+                                     ∀b,f. ⬇*[b,f] L1 ≘ K1 → ⬇*[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
 [ elim (coafter_inv_xxn … H) [ |*: // ] -H #g #g1 #Hg2 #H1 #H2 destruct
@@ -87,9 +87,9 @@ lemma sex_liftable_co_dedropable_sn: ∀RN,RP. (∀L. reflexive … (RN L)) →
 ]
 qed-.
 
-fact sex_dropable_dx_aux: ∀RN,RP,b,f,L2,K2. ⬇*[b, f] L2 ≘ K2 → 𝐔⦃f⦄ →
-                          ∀f2,L1. L1 ⪤[RN, RP, f2] L2 → ∀f1. f ~⊚ f1 ≘ f2 →
-                          ∃∃K1. ⬇*[b, f] L1 ≘ K1 & K1 ⪤[RN, RP, f1] K2.
+fact sex_dropable_dx_aux: ∀RN,RP,b,f,L2,K2. ⬇*[b,f] L2 ≘ K2 → 𝐔⦃f⦄ →
+                          ∀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/
@@ -113,10 +113,10 @@ lemma sex_co_dropable_dx: ∀RN,RP. co_dropable_dx (sex RN RP).
 /2 width=5 by sex_dropable_dx_aux/ qed-.
 
 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⦄ →
+                           ∀f2,L1,L2. L1 ⪤[RN,RP,f2] L2 →
+                           ∀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
@@ -124,30 +124,30 @@ elim (sex_co_dropable_sn … HLK1 … Hf … HL12 … Hf2) -L1 -f2 -Hf
 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⦄ →
+                           ∀f2,L1,L2. L1 ⪤[RN,RP,f2] L2 →
+                           ∀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
 #I2 #K2 #HK12 #HI12 #H destruct /2 width=5 by ex3_2_intro/
 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⦄ →
+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⦄ →
                             ∀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
 #I1 #K1 #HK12 #HI12 #H destruct /2 width=5 by ex3_2_intro/
 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⦄ →
+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⦄ →
                             ∀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
@@ -156,10 +156,10 @@ 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 →
+                            ∀f1,K1,K2. K1 ⪤[RN,RP,f1] K2 →
+                            ∀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
@@ -168,19 +168,19 @@ 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 →
+                            ∀f1,K1,K2. K1 ⪤[RN,RP,f1] K2 →
+                            ∀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: ∀RN,RP,b,f1,L1. ⬇*[b, f1] L1 ≘ ⋆ → 𝐔⦃f1⦄ →
-                            ∀f,L2. L1 ⪤[RN, RP, f] L2 →
-                            ∀f2. f1 ~⊚ f2 ≘f → ⬇*[b, f1] L2 ≘ ⋆.
+lemma drops_atom2_sex_conf: ∀RN,RP,b,f1,L1. ⬇*[b,f1] L1 ≘ ⋆ → 𝐔⦃f1⦄ →
+                            ∀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
 elim (sex_co_dropable_sn … H1 … H2 … H3) // -H1 -H2 -H3 -Hf1
 #L #H #HL2 lapply (sex_inv_atom1 … H) -H //