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14
15 include "ground/arith/ynat_succ.ma".
16 include "ground/arith/ynat_le_lminus.ma".
17
18 (* ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY ****************************)
19
20 (* Constructions with ylminus and ysucc *************************************)
21
22 (*** yminus_succ1_inj *)
23 lemma ylminus_succ_sn (x) (n):
24       yinj_nat n ≤ x → ↑(x - n) = ↑x - n.
25 #x @(ynat_split_nat_inf … x) -x //
26 #m #n #Hnm
27 <ylminus_inj_sn <ysucc_inj <ysucc_inj <ylminus_inj_sn
28 <nminus_succ_sn /2 width=1 by yle_inv_inj_bi/
29 qed-.