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14
15 include "ground/arith/pnat_plus.ma".
16 include "ground/arith/pnat_le.ma".
17
18 (* ORDER FOR POSITIVE INTEGERS **********************************************)
19
20 (* Constructions with pplus *************************************************)
21
22 lemma ple_plus_bi_dx (p) (q1) (q2): q1 ≤ q2 → q1 + p ≤ q2 + p.
23 #p #q1 #q2 #H elim H -q2 /2 width=3 by ple_trans/
24 qed.
25
26 lemma ple_plus_bi_sn (p) (q1) (q2): q1 ≤ q2 → p + q1 ≤ p + q2.
27 #p #q1 #q2 #H <pplus_comm <pplus_comm in ⊢ (??%);
28 /2 width=1 by ple_plus_bi_dx/
29 qed.