matita/contribs/RELATIONAL/NLE/nplus.ma

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  14
  15
  16
  17 include "NLE/defs.ma".
  18
  19 theorem nle_nplus: \forall p, q, r. (p + q == r) \to q <= r.
  20  intros. elim H; clear H q r; autobatch.
  21 qed.
  22
  23 axiom nle_nplus_comp: \forall x1, x2, x3. (x1 + x2 == x3) \to
  24                       \forall y1, y2, y3. (y1 + y2 == y3) \to
  25                       x1 <= y1 \to x2 <= y2 \to x3 <= y3.
  26
  27 axiom nle_nplus_comp_lt_2: \forall x1, x2, x3. (x1 + x2 == x3) \to
  28                            \forall y1, y2, y3. (y1 + y2 == y3) \to
  29                            x1 <= y1 \to x2 < y2 \to x3 < y3.