interpretation "ynat successor" 'Successor m = (ysucc m).
+lemma ysucc_inj: ∀m:nat. ⫯m = S m.
+// qed.
+
+lemma ysucc_Y: ⫯(∞) = ∞.
+// qed.
+
(* Properties ***************************************************************)
lemma ypred_succ: ∀m. ⫰⫯m = m.
(* Inversion lemmas *********************************************************)
-lemma ysucc_inj: ∀m,n. ⫯m = ⫯n → m = n.
+lemma ysucc_inv_inj: ∀m,n. ⫯m = ⫯n → m = n.
#m #n #H <(ypred_succ m) <(ypred_succ n) //
qed-.
lemma ysucc_inv_refl: ∀m. ⫯m = m → m = ∞.
-* // normalize
+* //
#m #H lapply (yinj_inj … H) -H (**) (* destruct lemma needed *)
#H elim (lt_refl_false m) //
qed-.