update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / rtmap_sdj.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sdj.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sdj.ma
index 99c6915dbcd38b8485a7bb20eedd2cf69b8a82fb..330ad6e98104d133a058d4b940b828cd9a5960ab 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sdj.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sdj.ma
@@ -18,9 +18,9 @@ include "ground_2/relocation/rtmap_isid.ma".
 (* RELOCATION MAP ***********************************************************)
 
 coinductive sdj: relation rtmap ≝
-| sdj_pp: â\88\80f1,f2,g1,g2. sdj f1 f2 â\86\92 â\86\91f1 = g1 â\86\92 â\86\91f2 = g2 → sdj g1 g2
-| sdj_np: â\88\80f1,f2,g1,g2. sdj f1 f2 â\86\92 ⫯f1 = g1 â\86\92 â\86\91f2 = g2 → sdj g1 g2
-| sdj_pn: â\88\80f1,f2,g1,g2. sdj f1 f2 â\86\92 â\86\91f1 = g1 â\86\92 ⫯f2 = g2 → sdj g1 g2
+| sdj_pp: â\88\80f1,f2,g1,g2. sdj f1 f2 â\86\92 ⫯f1 = g1 â\86\92 ⫯f2 = g2 → sdj g1 g2
+| sdj_np: â\88\80f1,f2,g1,g2. sdj f1 f2 â\86\92 â\86\91f1 = g1 â\86\92 ⫯f2 = g2 → sdj g1 g2
+| sdj_pn: â\88\80f1,f2,g1,g2. sdj f1 f2 â\86\92 ⫯f1 = g1 â\86\92 â\86\91f2 = g2 → sdj g1 g2
 .
 
 interpretation "disjointness (rtmap)"
@@ -49,7 +49,7 @@ qed-.
 
 (* Basic inversion lemmas ***************************************************)
 
-lemma sdj_inv_pp: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1,f2. â\86\91f1 = g1 â\86\92 â\86\91f2 = g2 → f1 ∥ f2.
+lemma sdj_inv_pp: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1,f2. ⫯f1 = g1 â\86\92 ⫯f2 = g2 → f1 ∥ f2.
 #g1 #g2 * -g1 -g2
 #f1 #f2 #g1 #g2 #H #H1 #H2 #x1 #x2 #Hx1 #Hx2 destruct
 [ lapply (injective_push … Hx1) -Hx1
@@ -59,7 +59,7 @@ lemma sdj_inv_pp: ∀g1,g2. g1 ∥ g2 → ∀f1,f2. ↑f1 = g1 → ↑f2 = g2 
 ]
 qed-.
 
-lemma sdj_inv_np: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1,f2. ⫯f1 = g1 â\86\92 â\86\91f2 = g2 → f1 ∥ f2.
+lemma sdj_inv_np: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1,f2. â\86\91f1 = g1 â\86\92 ⫯f2 = g2 → f1 ∥ f2.
 #g1 #g2 * -g1 -g2
 #f1 #f2 #g1 #g2 #H #H1 #H2 #x1 #x2 #Hx1 #Hx2 destruct
 [ elim (discr_next_push … Hx1)
@@ -69,7 +69,7 @@ lemma sdj_inv_np: ∀g1,g2. g1 ∥ g2 → ∀f1,f2. ⫯f1 = g1 → ↑f2 = g2 
 ]
 qed-.
 
-lemma sdj_inv_pn: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1,f2. â\86\91f1 = g1 â\86\92 ⫯f2 = g2 → f1 ∥ f2.
+lemma sdj_inv_pn: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1,f2. ⫯f1 = g1 â\86\92 â\86\91f2 = g2 → f1 ∥ f2.
 #g1 #g2 * -g1 -g2
 #f1 #f2 #g1 #g2 #H #H1 #H2 #x1 #x2 #Hx1 #Hx2 destruct
 [ elim (discr_next_push … Hx2)
@@ -79,7 +79,7 @@ lemma sdj_inv_pn: ∀g1,g2. g1 ∥ g2 → ∀f1,f2. ↑f1 = g1 → ⫯f2 = g2 
 ]
 qed-.
 
-lemma sdj_inv_nn: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1,f2. ⫯f1 = g1 â\86\92 ⫯f2 = g2 → ⊥.
+lemma sdj_inv_nn: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1,f2. â\86\91f1 = g1 â\86\92 â\86\91f2 = g2 → ⊥.
 #g1 #g2 * -g1 -g2
 #f1 #f2 #g1 #g2 #H #H1 #H2 #x1 #x2 #Hx1 #Hx2 destruct
 [ elim (discr_next_push … Hx1)
@@ -90,33 +90,33 @@ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma sdj_inv_nx: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1. ⫯f1 = g1 →
-                  â\88\83â\88\83f2. f1 â\88¥ f2 & â\86\91f2 = g2.
+lemma sdj_inv_nx: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1. â\86\91f1 = g1 →
+                  â\88\83â\88\83f2. f1 â\88¥ f2 & ⫯f2 = g2.
 #g1 #g2 elim (pn_split g2) * #f2 #H2 #H #f1 #H1
 [ lapply (sdj_inv_np … H … H1 H2) -H /2 width=3 by ex2_intro/
 | elim (sdj_inv_nn … H … H1 H2)
 ]
 qed-.
 
-lemma sdj_inv_xn: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f2. ⫯f2 = g2 →
-                  â\88\83â\88\83f1. f1 â\88¥ f2 & â\86\91f1 = g1.
+lemma sdj_inv_xn: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f2. â\86\91f2 = g2 →
+                  â\88\83â\88\83f1. f1 â\88¥ f2 & ⫯f1 = g1.
 #g1 #g2 elim (pn_split g1) * #f1 #H1 #H #f2 #H2
 [ lapply (sdj_inv_pn … H … H1 H2) -H /2 width=3 by ex2_intro/
 | elim (sdj_inv_nn … H … H1 H2)
 ]
 qed-.
 
-lemma sdj_inv_xp: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f2. â\86\91f2 = g2 →
-                  â\88¨â\88¨ â\88\83â\88\83f1. f1 â\88¥ f2 & â\86\91f1 = g1
-                   | â\88\83â\88\83f1. f1 â\88¥ f2 & ⫯f1 = g1.
+lemma sdj_inv_xp: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f2. ⫯f2 = g2 →
+                  â\88¨â\88¨ â\88\83â\88\83f1. f1 â\88¥ f2 & ⫯f1 = g1
+                   | â\88\83â\88\83f1. f1 â\88¥ f2 & â\86\91f1 = g1.
 #g1 #g2 elim (pn_split g1) * #f1 #H1 #H #f2 #H2
 [ lapply (sdj_inv_pp … H … H1 H2) | lapply (sdj_inv_np … H … H1 H2) ] -H -H2
 /3 width=3 by ex2_intro, or_introl, or_intror/
 qed-.
 
-lemma sdj_inv_px: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1. â\86\91f1 = g1 →
-                  â\88¨â\88¨ â\88\83â\88\83f2. f1 â\88¥ f2 & â\86\91f2 = g2
-                   | â\88\83â\88\83f2. f1 â\88¥ f2 & ⫯f2 = g2.
+lemma sdj_inv_px: â\88\80g1,g2. g1 â\88¥ g2 â\86\92 â\88\80f1. ⫯f1 = g1 →
+                  â\88¨â\88¨ â\88\83â\88\83f2. f1 â\88¥ f2 & ⫯f2 = g2
+                   | â\88\83â\88\83f2. f1 â\88¥ f2 & â\86\91f2 = g2.
 #g1 #g2 elim (pn_split g2) * #f2 #H2 #H #f1 #H1
 [ lapply (sdj_inv_pp … H … H1 H2) | lapply (sdj_inv_pn … H … H1 H2) ] -H -H1
 /3 width=3 by ex2_intro, or_introl, or_intror/
@@ -124,13 +124,13 @@ qed-.
 
 (* Properties with isid *****************************************************)
 
-corec lemma sdj_isid_dx: â\88\80f2. ð\9d\90\88â¦\83f2â¦\84 → ∀f1. f1 ∥ f2.
+corec lemma sdj_isid_dx: â\88\80f2. ð\9d\90\88â\9dªf2â\9d« → ∀f1. f1 ∥ f2.
 #f2 * -f2
 #f2 #g2 #Hf2 #H2 #f1 cases (pn_split f1) *
 /3 width=5 by sdj_np, sdj_pp/
 qed.
 
-corec lemma sdj_isid_sn: â\88\80f1. ð\9d\90\88â¦\83f1â¦\84 → ∀f2. f1 ∥ f2.
+corec lemma sdj_isid_sn: â\88\80f1. ð\9d\90\88â\9dªf1â\9d« → ∀f2. f1 ∥ f2.
 #f1 * -f1
 #f1 #g1 #Hf1 #H1 #f2 cases (pn_split f2) *
 /3 width=5 by sdj_pn, sdj_pp/
@@ -138,7 +138,7 @@ qed.
 
 (* Inversion lemmas with isid ***********************************************)
 
-corec lemma sdj_inv_refl: â\88\80f. f â\88¥ f â\86\92  ð\9d\90\88â¦\83fâ¦\84.
+corec lemma sdj_inv_refl: â\88\80f. f â\88¥ f â\86\92  ð\9d\90\88â\9dªfâ\9d«.
 #f cases (pn_split f) * #g #Hg #H
 [ lapply (sdj_inv_pp … H … Hg Hg) -H /3 width=3 by isid_push/
 | elim (sdj_inv_nn … H … Hg Hg)