- first results on strongly normalizing local environments

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_succ.ma b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_succ.ma
index d0ed1d6bde893ebb416f2aed10c8027059a43d54..a8d1946bea235170f6405cdcc962f660c1e789ae 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_succ.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_succ.ma
@@ -30,6 +30,19 @@ interpretation "ynat successor" 'Successor m = (ysucc m).
 lemma ypred_succ: ∀m. ⫰⫯m = m.
 * // qed.
 
+lemma ynat_cases: ∀n:ynat. n = 0 ∨ ∃m. n = ⫯m.
+*
+[ * /2 width=1 by or_introl/
+  #n @or_intror @(ex_intro … n) // (**) (* explicit constructor *)
+| @or_intror @(ex_intro … (∞)) // (**) (* explicit constructor *)
+]
+qed-.
+
+lemma ysucc_iter_Y: ∀m. ysucc^m (∞) = ∞.
+#m elim m -m //
+#m #IHm whd in ⊢ (??%?); >IHm //
+qed.
+
 (* Inversion lemmas *********************************************************)
 
 lemma ysucc_inj: ∀m,n. ⫯m = ⫯n → m = n.
@@ -53,3 +66,19 @@ qed-.
 lemma ysucc_inv_inj_dx: ∀m2,n1. ⫯n1 = yinj m2  →
                         ∃∃m1. n1 = yinj m1 & m2 = S m1.
 /2 width=1 by ysucc_inv_inj_sn/ qed-.
+
+lemma ysucc_inv_Y_sn: ∀m. ∞ = ⫯m → m = ∞.
+* // normalize
+#m #H destruct
+qed-.
+
+lemma ysucc_inv_Y_dx: ∀m. ⫯m = ∞ → m = ∞.
+/2 width=1 by ysucc_inv_Y_sn/ qed-.
+
+lemma ysucc_inv_O_sn: ∀m. yinj 0 = ⫯m → ⊥. (**) (* explicit coercion *)
+#m #H elim (ysucc_inv_inj_sn … H) -H
+#n #_ #H destruct
+qed-.
+
+lemma ysucc_inv_O_dx: ∀m. ⫯m = 0 → ⊥.
+/2 width=2 by ysucc_inv_O_sn/ qed-.