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4 (* ||A|| A project by Andrea Asperti *)
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7 (* ||T|| The HELM team. *)
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15 include "ground/arith/ynat_le_pred_succ.ma".
16 include "ground/arith/ynat_lt_pred_succ.ma".
18 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
20 (* Constructions with yle and ypred and ysucc *******************************)
22 (*** yle_inv_succ_sn_lt yle_inv_succ1_lt *)
23 lemma le_succ_sn_ylt (x) (y):
24 ↑x ≤ y → ∧∧ x ≤ ↓y & 𝟎 < y.
25 #x #y #H elim (yle_inv_succ_sn … H) -H
26 /4 width=2 by ylt_zero_sn, conj/