some restyling ...

[helm.git] / matita / matita / contribs / lambdadelta / static_2 / static / rex_drops.ma

diff --git a/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma b/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma
index 60e335d57caf2dde6e773d068f689010b81e3efd..5a04668001eb7d91e8583ab51324841ff0bca211 100644 (file)
--- a/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma
+++ b/matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma
@@ -20,19 +20,19 @@ include "static_2/static/rex.ma".
 (* GENERIC EXTENSION ON REFERRED ENTRIES OF A CONTEXT-SENSITIVE REALTION ****)
 
 definition f_dedropable_sn: predicate (relation3 lenv term term) ≝
-                            λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 →
-                            ∀K2,T. K1 ⪤[R, T] K2 → ∀U. ⬆*[f] T ≘ U →
-                            ∃∃L2. L1 ⪤[R, U] L2 & ⬇*[b, f] L2 ≘ K2 & L1 ≡[f] L2.
+                            λR. ∀b,f,L1,K1. ⬇*[b,f] L1 ≘ K1 →
+                            ∀K2,T. K1 ⪤[R,T] K2 → ∀U. ⬆*[f] T ≘ U →
+                            ∃∃L2. L1 ⪤[R,U] L2 & ⬇*[b,f] L2 ≘ K2 & L1 ≡[f] L2.
 
 definition f_dropable_sn: predicate (relation3 lenv term term) ≝
-                          λR. ∀b,f,L1,K1. ⬇*[b, f] L1 ≘ K1 → 𝐔⦃f⦄ →
-                          ∀L2,U. L1 ⪤[R, U] L2 → ∀T. ⬆*[f] T ≘ U →
-                          ∃∃K2. K1 ⪤[R, T] K2 & ⬇*[b, f] L2 ≘ K2.
+                          λR. ∀b,f,L1,K1. ⬇*[b,f] L1 ≘ K1 → 𝐔⦃f⦄ →
+                          ∀L2,U. L1 ⪤[R,U] L2 → ∀T. ⬆*[f] T ≘ U →
+                          ∃∃K2. K1 ⪤[R,T] K2 & ⬇*[b,f] L2 ≘ K2.
 
 definition f_dropable_dx: predicate (relation3 lenv term term) ≝
-                          λR. ∀L1,L2,U. L1 ⪤[R, U] L2 →
-                          ∀b,f,K2. ⬇*[b, f] L2 ≘ K2 → 𝐔⦃f⦄ → ∀T. ⬆*[f] T ≘ U →
-                          ∃∃K1. ⬇*[b, f] L1 ≘ K1 & K1 ⪤[R, T] K2.
+                          λR. ∀L1,L2,U. L1 ⪤[R,U] L2 →
+                          ∀b,f,K2. ⬇*[b,f] L2 ≘ K2 → 𝐔⦃f⦄ → ∀T. ⬆*[f] T ≘ U →
+                          ∃∃K1. ⬇*[b,f] L1 ≘ K1 & K1 ⪤[R,T] K2.
 
 definition f_transitive_next: relation3 … ≝ λR1,R2,R3.
                               ∀f,L,T. L ⊢ 𝐅*⦃T⦄ ≘ f →
@@ -87,48 +87,48 @@ elim (sex_co_dropable_dx … HL12 … HLK2 … H2f) -L2
 qed-.
 
 (* Basic_2A1: uses: llpx_sn_inv_lift_O *)
-lemma rex_inv_lifts_bi: ∀R,L1,L2,U. L1 ⪤[R, U] L2 → ∀b,f. 𝐔⦃f⦄ → 
-                        ∀K1,K2. ⬇*[b, f] L1 ≘ K1 → ⬇*[b, f] L2 ≘ K2 →
-                        ∀T. ⬆*[f] T ≘ U → K1 ⪤[R, T] K2.
+lemma rex_inv_lifts_bi: ∀R,L1,L2,U. L1 ⪤[R,U] L2 → ∀b,f. 𝐔⦃f⦄ → 
+                        ∀K1,K2. ⬇*[b,f] L1 ≘ K1 → ⬇*[b,f] L2 ≘ K2 →
+                        ∀T. ⬆*[f] T ≘ U → K1 ⪤[R,T] K2.
 #R #L1 #L2 #U #HL12 #b #f #Hf #K1 #K2 #HLK1 #HLK2 #T #HTU
 elim (rex_dropable_sn … HLK1 … HL12 … HTU) -L1 -U // #Y #HK12 #HY
 lapply (drops_mono … HY … HLK2) -b -f -L2 #H destruct //
 qed-.
 
-lemma rex_inv_lref_pair_sn: ∀R,L1,L2,i. L1 ⪤[R, #i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
-                            ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ⪤[R, V1] K2 & R K1 V1 V2.
+lemma rex_inv_lref_pair_sn: ∀R,L1,L2,i. L1 ⪤[R,#i] L2 → ∀I,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 →
+                            ∃∃K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 & K1 ⪤[R,V1] K2 & R K1 V1 V2.
 #R #L1 #L2 #i #HL12 #I #K1 #V1 #HLK1 elim (rex_dropable_sn … HLK1 … HL12 (#0)) -HLK1 -HL12 //
 #Y #HY #HLK2 elim (rex_inv_zero_pair_sn … HY) -HY
 #K2 #V2 #HK12 #HV12 #H destruct /2 width=5 by ex3_2_intro/
 qed-.
 
-lemma rex_inv_lref_pair_dx: ∀R,L1,L2,i. L1 ⪤[R, #i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
-                            ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ⪤[R, V1] K2 & R K1 V1 V2.
+lemma rex_inv_lref_pair_dx: ∀R,L1,L2,i. L1 ⪤[R,#i] L2 → ∀I,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I}V2 →
+                            ∃∃K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I}V1 & K1 ⪤[R,V1] K2 & R K1 V1 V2.
 #R #L1 #L2 #i #HL12 #I #K2 #V2 #HLK2 elim (rex_dropable_dx … HL12 … HLK2 … (#0)) -HLK2 -HL12 //
 #Y #HLK1 #HY elim (rex_inv_zero_pair_dx … HY) -HY
 #K1 #V1 #HK12 #HV12 #H destruct /2 width=5 by ex3_2_intro/
 qed-.
 
 lemma rex_inv_lref_pair_bi (R) (L1) (L2) (i):
-                           L1 ⪤[R, #i] L2 →
+                           L1 ⪤[R,#i] L2 →
                            ∀I1,K1,V1. ⬇*[i] L1 ≘ K1.ⓑ{I1}V1 →
                            ∀I2,K2,V2. ⬇*[i] L2 ≘ K2.ⓑ{I2}V2 →
-                           ∧∧ K1 ⪤[R, V1] K2 & R K1 V1 V2 & I1 = I2.
+                           ∧∧ K1 ⪤[R,V1] K2 & R K1 V1 V2 & I1 = I2.
 #R #L1 #L2 #i #H12 #I1 #K1 #V1 #H1 #I2 #K2 #V2 #H2
 elim (rex_inv_lref_pair_sn … H12 … H1) -L1 #Y2 #X2 #HLY2 #HK12 #HV12
 lapply (drops_mono … HLY2 … H2) -HLY2 -H2 #H destruct
 /2 width=1 by and3_intro/
 qed-.
 
-lemma rex_inv_lref_unit_sn: ∀R,L1,L2,i. L1 ⪤[R, #i] L2 → ∀I,K1. ⬇*[i] L1 ≘ K1.ⓤ{I} →
-                            ∃∃f,K2. ⬇*[i] L2 ≘ K2.ⓤ{I} & K1 ⪤[cext2 R, cfull, f] K2 & 𝐈⦃f⦄.
+lemma rex_inv_lref_unit_sn: ∀R,L1,L2,i. L1 ⪤[R,#i] L2 → ∀I,K1. ⬇*[i] L1 ≘ K1.ⓤ{I} →
+                            ∃∃f,K2. ⬇*[i] L2 ≘ K2.ⓤ{I} & K1 ⪤[cext2 R,cfull,f] K2 & 𝐈⦃f⦄.
 #R #L1 #L2 #i #HL12 #I #K1 #HLK1 elim (rex_dropable_sn … HLK1 … HL12 (#0)) -HLK1 -HL12 //
 #Y #HY #HLK2 elim (rex_inv_zero_unit_sn … HY) -HY
 #f #K2 #Hf #HK12 #H destruct /2 width=5 by ex3_2_intro/
 qed-.
 
-lemma rex_inv_lref_unit_dx: ∀R,L1,L2,i. L1 ⪤[R, #i] L2 → ∀I,K2. ⬇*[i] L2 ≘ K2.ⓤ{I} →
-                            ∃∃f,K1. ⬇*[i] L1 ≘ K1.ⓤ{I} & K1 ⪤[cext2 R, cfull, f] K2 & 𝐈⦃f⦄.
+lemma rex_inv_lref_unit_dx: ∀R,L1,L2,i. L1 ⪤[R,#i] L2 → ∀I,K2. ⬇*[i] L2 ≘ K2.ⓤ{I} →
+                            ∃∃f,K1. ⬇*[i] L1 ≘ K1.ⓤ{I} & K1 ⪤[cext2 R,cfull,f] K2 & 𝐈⦃f⦄.
 #R #L1 #L2 #i #HL12 #I #K2 #HLK2 elim (rex_dropable_dx … HL12 … HLK2 … (#0)) -HLK2 -HL12 //
 #Y #HLK1 #HY elim (rex_inv_zero_unit_dx … HY) -HY
 #f #K2 #Hf #HK12 #H destruct /2 width=5 by ex3_2_intro/