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14
15 include "ground/arith/nat_minus_plus.ma".
16 include "ground/arith/ynat_plus.ma".
17 include "ground/arith/ynat_lminus_succ.ma".
18
19 (* LEFT SUBTRACTION FOR NON-NEGATIVE INTEGERS WITH INFINITY *****************)
20
21 (* Constructions with yplus *************************************************)
22
23 (*** yplus_minus *)
24 lemma ylminus_plus_sn_refl_sn (x) (n):
25       x = x + yinj_nat n - n.
26 #x @(ynat_split_nat_inf … x) -x //
27 #n <yplus_inf_sn //
28 qed.
29
30 (*** yminus_plus2 *)
31 lemma yminus_plus_dx (x:ynat) (n) (o):
32       x - n - o = x - (n + o).
33 #x @(ynat_split_nat_inf … x) -x //
34 qed.