#m >yminus_inj //
qed.
-lemma yminus_succ1_inj: ∀n:nat. ∀m:ynat. n ≤ m → ⫯m - n = ⫯(m - n).
+lemma yminus_succ1_inj: ∀n:nat. ∀m:ynat. n ≤ m → ⫯m - n = ⫯(m - n).
#n *
[ #m #Hmn >yminus_inj >yminus_inj
/4 width=1 by yle_inv_inj, plus_minus, eq_f/
]
qed-.
+lemma yminus_succ2: ∀y,x. x - ⫯y = ⫰(x-y).
+* //
+qed.
+
(* Properties on order ******************************************************)
lemma yle_minus_sn: ∀n,m. m - n ≤ m.