matita/matita/contribs/RELATIONAL/NLE/nplus.ma

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  14
  15
  16
  17 include "NLE/defs.ma".
  18
  19 theorem nle_nplus: ∀p, q, r. p ⊕ q ≍ r → q ≤ r.
  20  intros; elim H; clear H q r; autobatch.
  21 qed.
  22
  23 axiom nle_nplus_comp: ∀x1,x2,x3. x1 ⊕ x2 ≍ x3 → ∀y1,y2,y3. y1 ⊕ y2 ≍ y3 →
  24                       x1 ≤ y1 → x2 ≤ y2 → x3 ≤ y3.
  25
  26 axiom nle_nplus_comp_lt_2: ∀x1,x2,x3. x1 ⊕ x2 ≍ x3 → ∀y1,y2,y3. y1 ⊕ y2 ≍ y3 →
  27                            x1 ≤ y1 → x2 < y2 → x3 < y3.