milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / ynat / ynat_le.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_le.ma b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_le.ma
index 613a9793cb6a547b9e53ca49ce0307abaead7230..54e946e96ca40a4ace88868863b258d2ce282cd5 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_le.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_le.ma
@@ -46,7 +46,7 @@ fact yle_inv_O2_aux: ∀m:ynat. ∀x:ynat. m ≤ x → x = 0 → m = 0.
 #m #x * -m -x
 [ #m #n #Hmn #H destruct /3 width=1 by le_n_O_to_eq, eq_f/
 | #m #H destruct
-] 
+]
 qed-.
 
 lemma yle_inv_O2: ∀m:ynat. m ≤ 0 → m = 0.
@@ -83,7 +83,7 @@ qed-.
 
 (* Inversion lemmas on successor ********************************************)
 
-fact yle_inv_succ1_aux: ∀x,y. x ≤ y → ∀m. x = ⫯m → m ≤ ⫰y ∧ ⫯⫰y = y.
+fact yle_inv_succ1_aux: ∀x,y:ynat. x ≤ y → ∀m. x = ↑m → m ≤ ↓y ∧ ↑↓y = y.
 #x #y * -x -y
 [ #x #y #Hxy #m #H elim (ysucc_inv_inj_sn … H) -H
   #n #H1 #H2 destruct elim (le_inv_S1 … Hxy) -Hxy
@@ -92,14 +92,14 @@ fact yle_inv_succ1_aux: ∀x,y. x ≤ y → ∀m. x = ⫯m → m ≤ ⫰y ∧ 
 ]
 qed-.
 
-lemma yle_inv_succ1: ∀m,y. ⫯m ≤ y → m ≤ ⫰y ∧ ⫯⫰y = y.
+lemma yle_inv_succ1: ∀m,y:ynat. ↑m ≤ y → m ≤ ↓y ∧ ↑↓y = y.
 /2 width=3 by yle_inv_succ1_aux/ qed-.
 
-lemma yle_inv_succ: â\88\80m,n. ⫯m â\89¤ ⫯n → m ≤ n.
+lemma yle_inv_succ: â\88\80m,n. â\86\91m â\89¤ â\86\91n → m ≤ n.
 #m #n #H elim (yle_inv_succ1 … H) -H //
 qed-.
 
-lemma yle_inv_succ2: â\88\80x,y. x â\89¤ ⫯y â\86\92 â«°x ≤ y.
+lemma yle_inv_succ2: â\88\80x,y. x â\89¤ â\86\91y â\86\92 â\86\93x ≤ y.
 #x #y #Hxy elim (ynat_cases x)
 [ #H destruct //
 | * #m #H destruct /2 width=1 by yle_inv_succ/
@@ -108,35 +108,35 @@ qed-.
 
 (* Properties on predecessor ************************************************)
 
-lemma yle_pred_sn: â\88\80m,n. m â\89¤ n â\86\92 â«°m ≤ n.
+lemma yle_pred_sn: â\88\80m,n. m â\89¤ n â\86\92 â\86\93m ≤ n.
 #m #n * -m -n /3 width=3 by transitive_le, yle_inj/
 qed.
 
-lemma yle_refl_pred_sn: â\88\80x. â«°x ≤ x.
+lemma yle_refl_pred_sn: â\88\80x. â\86\93x ≤ x.
 /2 width=1 by yle_refl, yle_pred_sn/ qed.
 
-lemma yle_pred: â\88\80m,n. m â\89¤ n â\86\92 â«°m â\89¤ â«°n.
+lemma yle_pred: â\88\80m,n. m â\89¤ n â\86\92 â\86\93m â\89¤ â\86\93n.
 #m #n * -m -n /3 width=1 by yle_inj, monotonic_pred/
 qed.
 
 (* Properties on successor **************************************************)
 
-lemma yle_succ: â\88\80m,n. m â\89¤ n â\86\92 ⫯m â\89¤ ⫯n.
+lemma yle_succ: â\88\80m,n. m â\89¤ n â\86\92 â\86\91m â\89¤ â\86\91n.
 #m #n * -m -n /3 width=1 by yle_inj, le_S_S/
 qed.
 
-lemma yle_succ_dx: â\88\80m,n. m â\89¤ n â\86\92 m â\89¤ ⫯n.
+lemma yle_succ_dx: â\88\80m,n. m â\89¤ n â\86\92 m â\89¤ â\86\91n.
 #m #n * -m -n /3 width=1 by le_S, yle_inj/
 qed.
 
-lemma yle_refl_S_dx: â\88\80x. x â\89¤ ⫯x.
+lemma yle_refl_S_dx: â\88\80x. x â\89¤ â\86\91x.
 /2 width=1 by yle_succ_dx/ qed.
 
-lemma yle_refl_SP_dx: â\88\80x. x â\89¤ ⫯⫰x.
+lemma yle_refl_SP_dx: â\88\80x. x â\89¤ â\86\91â\86\93x.
 * // * //
 qed.
 
-lemma yle_succ2: â\88\80x,y. â«°x â\89¤ y â\86\92 x â\89¤ ⫯y.
+lemma yle_succ2: â\88\80x,y. â\86\93x â\89¤ y â\86\92 x â\89¤ â\86\91y.
 #x #y #Hxy elim (ynat_cases x)
 [ #H destruct //
 | * #m #H destruct /2 width=1 by yle_succ/
@@ -152,4 +152,4 @@ theorem yle_trans: Transitive … yle.
   /3 width=3 by transitive_le, yle_inj/ (**) (* full auto too slow *)
 | #x #z #H lapply (yle_inv_Y1 … H) //
 ]
-qed-. 
+qed-.