ground_2 milestone: multiple relocation with lists of booleans

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_pred.ma b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_pred.ma
index 1f14ea6c0c0f57522257d26b43870251eef35322..8d17df7ff8daabc1b28051b450cd5135cacda97c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_pred.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_pred.ma
@@ -20,16 +20,16 @@ include "ground_2/ynat/ynat.ma".
 
 (* the predecessor function *)
 definition ypred: ynat → ynat ≝ λm. match m with
-[ yinj m ⇒ pred m
+[ yinj m ⇒ ⫰m
 | Y      ⇒ Y
 ].
 
 interpretation "ynat predecessor" 'Predecessor m = (ypred m).
 
-lemma ypred_O: ⫰0 = 0.
+lemma ypred_O: ⫰(yinj 0) = yinj 0.
 // qed.
 
-lemma ypred_S: ∀m:nat. ⫰(S m) = m.
+lemma ypred_S: ∀m:nat. ⫰(⫯m) = yinj m.
 // qed.
 
 lemma ypred_Y: (⫰∞) = ∞.
@@ -37,7 +37,7 @@ lemma ypred_Y: (⫰∞) = ∞.
 
 (* Inversion lemmas *********************************************************)
 
-lemma ypred_inv_refl: ∀m. ⫰m = m → m = 0 ∨ m = ∞.
+lemma ypred_inv_refl: ∀m:ynat. ⫰m = m → m = 0 ∨ m = ∞.
 * // #m #H lapply (yinj_inj … H) -H (**) (* destruct lemma needed *)
 /4 width=1 by pred_inv_refl, or_introl, eq_f/
 qed-.