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17 include "NLE/defs.ma".
19 theorem nle_nplus: \forall p, q, r. (p + q == r) \to q <= r.
20 intros. elim H; clear H q r; autobatch.
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.
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.