update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sor.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sor.ma
index de0872c44e2d7c9133014c8d83540c18b03bb827..9191eb3212b6aa67185a8f444a3c7fc2fba45af8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sor.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sor.ma
@@ -310,19 +310,19 @@ qed.
 
 (* Properies with test for identity *****************************************)
 
-corec lemma sor_isid_sn: â\88\80f1. ð\9d\90\88â¦\83f1â¦\84 → ∀f2. f1 ⋓ f2 ≘ f2.
+corec lemma sor_isid_sn: â\88\80f1. ð\9d\90\88â\9dªf1â\9d« → ∀f2. f1 ⋓ f2 ≘ f2.
 #f1 * -f1
 #f1 #g1 #Hf1 #H1 #f2 cases (pn_split f2) *
 /3 width=7 by sor_pp, sor_pn/
 qed.
 
-corec lemma sor_isid_dx: â\88\80f2. ð\9d\90\88â¦\83f2â¦\84 → ∀f1. f1 ⋓ f2 ≘ f1.
+corec lemma sor_isid_dx: â\88\80f2. ð\9d\90\88â\9dªf2â\9d« → ∀f1. f1 ⋓ f2 ≘ f1.
 #f2 * -f2
 #f2 #g2 #Hf2 #H2 #f1 cases (pn_split f1) *
 /3 width=7 by sor_pp, sor_np/
 qed.
 
-lemma sor_isid: â\88\80f1,f2,f. ð\9d\90\88â¦\83f1â¦\84 â\86\92 ð\9d\90\88â¦\83f2â¦\84 â\86\92 ð\9d\90\88â¦\83fâ¦\84 → f1 ⋓ f2 ≘ f.
+lemma sor_isid: â\88\80f1,f2,f. ð\9d\90\88â\9dªf1â\9d« â\86\92 ð\9d\90\88â\9dªf2â\9d« â\86\92 ð\9d\90\88â\9dªfâ\9d« → f1 ⋓ f2 ≘ f.
 /4 width=3 by sor_eq_repl_back2, sor_eq_repl_back1, isid_inv_eq_repl/ qed.
 
 (* Inversion lemmas with tail ***********************************************)
@@ -339,35 +339,35 @@ qed-.
 
 (* Inversion lemmas with test for identity **********************************)
 
-lemma sor_isid_inv_sn: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â¦\83f1â¦\84 → f2 ≡ f.
+lemma sor_isid_inv_sn: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â\9dªf1â\9d« → f2 ≡ f.
 /3 width=4 by sor_isid_sn, sor_mono/
 qed-.
 
-lemma sor_isid_inv_dx: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â¦\83f2â¦\84 → f1 ≡ f.
+lemma sor_isid_inv_dx: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â\9dªf2â\9d« → f1 ≡ f.
 /3 width=4 by sor_isid_dx, sor_mono/
 qed-.
 
-corec lemma sor_fwd_isid1: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â¦\83fâ¦\84 â\86\92 ð\9d\90\88â¦\83f1â¦\84.
+corec lemma sor_fwd_isid1: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â\9dªfâ\9d« â\86\92 ð\9d\90\88â\9dªf1â\9d«.
 #f1 #f2 #f * -f1 -f2 -f
 #f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H #Hg
 [ /4 width=6 by isid_inv_push, isid_push/ ]
 cases (isid_inv_next … Hg … H)
 qed-.
 
-corec lemma sor_fwd_isid2: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â¦\83fâ¦\84 â\86\92 ð\9d\90\88â¦\83f2â¦\84.
+corec lemma sor_fwd_isid2: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â\9dªfâ\9d« â\86\92 ð\9d\90\88â\9dªf2â\9d«.
 #f1 #f2 #f * -f1 -f2 -f
 #f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H #Hg
 [ /4 width=6 by isid_inv_push, isid_push/ ]
 cases (isid_inv_next … Hg … H)
 qed-.
 
-lemma sor_inv_isid3: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â¦\83fâ¦\84 â\86\92 ð\9d\90\88â¦\83f1â¦\84 â\88§ ð\9d\90\88â¦\83f2â¦\84.
+lemma sor_inv_isid3: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\88â\9dªfâ\9d« â\86\92 ð\9d\90\88â\9dªf1â\9d« â\88§ ð\9d\90\88â\9dªf2â\9d«.
 /3 width=4 by sor_fwd_isid2, sor_fwd_isid1, conj/ qed-.
 
 (* Properties with finite colength assignment *******************************)
 
-lemma sor_fcla_ex: â\88\80f1,n1. ð\9d\90\82â¦\83f1â¦\84 â\89\98 n1 â\86\92 â\88\80f2,n2. ð\9d\90\82â¦\83f2â¦\84 ≘ n2 →
-                   â\88\83â\88\83f,n. f1 â\8b\93 f2 â\89\98 f & ð\9d\90\82â¦\83fâ¦\84 ≘ n & (n1 ∨ n2) ≤ n & n ≤ n1 + n2.
+lemma sor_fcla_ex: â\88\80f1,n1. ð\9d\90\82â\9dªf1â\9d« â\89\98 n1 â\86\92 â\88\80f2,n2. ð\9d\90\82â\9dªf2â\9d« ≘ n2 →
+                   â\88\83â\88\83f,n. f1 â\8b\93 f2 â\89\98 f & ð\9d\90\82â\9dªfâ\9d« ≘ n & (n1 ∨ n2) ≤ n & n ≤ n1 + n2.
 #f1 #n1 #Hf1 elim Hf1 -f1 -n1 /3 width=6 by sor_isid_sn, ex4_2_intro/
 #f1 #n1 #Hf1 #IH #f2 #n2 * -f2 -n2 /3 width=6 by fcla_push, fcla_next, ex4_2_intro, sor_isid_dx/
 #f2 #n2 #Hf2 elim (IH … Hf2) -IH -Hf2 -Hf1 [2,4: #f #n <plus_n_Sm ] (**) (* full auto fails *)
@@ -378,16 +378,16 @@ lemma sor_fcla_ex: ∀f1,n1. 𝐂⦃f1⦄ ≘ n1 → ∀f2,n2. 𝐂⦃f2⦄ ≘
 ]
 qed-.
 
-lemma sor_fcla: â\88\80f1,n1. ð\9d\90\82â¦\83f1â¦\84 â\89\98 n1 â\86\92 â\88\80f2,n2. ð\9d\90\82â¦\83f2â¦\84 ≘ n2 → ∀f. f1 ⋓ f2 ≘ f →
-                â\88\83â\88\83n. ð\9d\90\82â¦\83fâ¦\84 ≘ n & (n1 ∨ n2) ≤ n & n ≤ n1 + n2.
+lemma sor_fcla: â\88\80f1,n1. ð\9d\90\82â\9dªf1â\9d« â\89\98 n1 â\86\92 â\88\80f2,n2. ð\9d\90\82â\9dªf2â\9d« ≘ n2 → ∀f. f1 ⋓ f2 ≘ f →
+                â\88\83â\88\83n. ð\9d\90\82â\9dªfâ\9d« ≘ n & (n1 ∨ n2) ≤ n & n ≤ n1 + n2.
 #f1 #n1 #Hf1 #f2 #n2 #Hf2 #f #Hf elim (sor_fcla_ex … Hf1 … Hf2) -Hf1 -Hf2
 /4 width=6 by sor_mono, fcla_eq_repl_back, ex3_intro/
 qed-.
 
 (* Forward lemmas with finite colength **************************************)
 
-lemma sor_fwd_fcla_sn_ex: â\88\80f,n. ð\9d\90\82â¦\83fâ¦\84 ≘ n → ∀f1,f2. f1 ⋓ f2 ≘ f →
-                          â\88\83â\88\83n1.  ð\9d\90\82â¦\83f1â¦\84 ≘ n1 & n1 ≤ n.
+lemma sor_fwd_fcla_sn_ex: â\88\80f,n. ð\9d\90\82â\9dªfâ\9d« ≘ n → ∀f1,f2. f1 ⋓ f2 ≘ f →
+                          â\88\83â\88\83n1.  ð\9d\90\82â\9dªf1â\9d« ≘ n1 & n1 ≤ n.
 #f #n #H elim H -f -n
 [ /4 width=4 by sor_fwd_isid1, fcla_isid, ex2_intro/
 | #f #n #_ #IH #f1 #f2 #H
@@ -399,37 +399,37 @@ lemma sor_fwd_fcla_sn_ex: ∀f,n. 𝐂⦃f⦄ ≘ n → ∀f1,f2. f1 ⋓ f2 ≘
 ]
 qed-.
 
-lemma sor_fwd_fcla_dx_ex: â\88\80f,n. ð\9d\90\82â¦\83fâ¦\84 ≘ n → ∀f1,f2. f1 ⋓ f2 ≘ f →
-                          â\88\83â\88\83n2.  ð\9d\90\82â¦\83f2â¦\84 ≘ n2 & n2 ≤ n.
+lemma sor_fwd_fcla_dx_ex: â\88\80f,n. ð\9d\90\82â\9dªfâ\9d« ≘ n → ∀f1,f2. f1 ⋓ f2 ≘ f →
+                          â\88\83â\88\83n2.  ð\9d\90\82â\9dªf2â\9d« ≘ n2 & n2 ≤ n.
 /3 width=4 by sor_fwd_fcla_sn_ex, sor_comm/ qed-.
 
 (* Properties with test for finite colength *********************************)
 
-lemma sor_isfin_ex: â\88\80f1,f2. ð\9d\90\85â¦\83f1â¦\84 â\86\92 ð\9d\90\85â¦\83f2â¦\84 â\86\92 â\88\83â\88\83f. f1 â\8b\93 f2 â\89\98 f & ð\9d\90\85â¦\83fâ¦\84.
+lemma sor_isfin_ex: â\88\80f1,f2. ð\9d\90\85â\9dªf1â\9d« â\86\92 ð\9d\90\85â\9dªf2â\9d« â\86\92 â\88\83â\88\83f. f1 â\8b\93 f2 â\89\98 f & ð\9d\90\85â\9dªfâ\9d«.
 #f1 #f2 * #n1 #H1 * #n2 #H2 elim (sor_fcla_ex … H1 … H2) -H1 -H2
 /3 width=4 by ex2_intro, ex_intro/
 qed-.
 
-lemma sor_isfin: â\88\80f1,f2. ð\9d\90\85â¦\83f1â¦\84 â\86\92 ð\9d\90\85â¦\83f2â¦\84 â\86\92 â\88\80f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\85â¦\83fâ¦\84.
+lemma sor_isfin: â\88\80f1,f2. ð\9d\90\85â\9dªf1â\9d« â\86\92 ð\9d\90\85â\9dªf2â\9d« â\86\92 â\88\80f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\85â\9dªfâ\9d«.
 #f1 #f2 #Hf1 #Hf2 #f #Hf elim (sor_isfin_ex … Hf1 … Hf2) -Hf1 -Hf2
 /3 width=6 by sor_mono, isfin_eq_repl_back/
 qed-.
 
 (* Forward lemmas with test for finite colength *****************************)
 
-lemma sor_fwd_isfin_sn: â\88\80f. ð\9d\90\85â¦\83fâ¦\84 â\86\92 â\88\80f1,f2. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\85â¦\83f1â¦\84.
+lemma sor_fwd_isfin_sn: â\88\80f. ð\9d\90\85â\9dªfâ\9d« â\86\92 â\88\80f1,f2. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\85â\9dªf1â\9d«.
 #f * #n #Hf #f1 #f2 #H
 elim (sor_fwd_fcla_sn_ex … Hf … H) -f -f2 /2 width=2 by ex_intro/
 qed-.
 
-lemma sor_fwd_isfin_dx: â\88\80f. ð\9d\90\85â¦\83fâ¦\84 â\86\92 â\88\80f1,f2. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\85â¦\83f2â¦\84.
+lemma sor_fwd_isfin_dx: â\88\80f. ð\9d\90\85â\9dªfâ\9d« â\86\92 â\88\80f1,f2. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\85â\9dªf2â\9d«.
 #f * #n #Hf #f1 #f2 #H
 elim (sor_fwd_fcla_dx_ex … Hf … H) -f -f1 /2 width=2 by ex_intro/
 qed-.
 
 (* Inversion lemmas with test for finite colength ***************************)
 
-lemma sor_inv_isfin3: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\85â¦\83fâ¦\84 â\86\92 ð\9d\90\85â¦\83f1â¦\84 â\88§ ð\9d\90\85â¦\83f2â¦\84.
+lemma sor_inv_isfin3: â\88\80f1,f2,f. f1 â\8b\93 f2 â\89\98 f â\86\92 ð\9d\90\85â\9dªfâ\9d« â\86\92 ð\9d\90\85â\9dªf1â\9d« â\88§ ð\9d\90\85â\9dªf2â\9d«.
 /3 width=4 by sor_fwd_isfin_dx, sor_fwd_isfin_sn, conj/ qed-.
 
 (* Inversion lemmas with inclusion ******************************************)