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17 include "NLE/defs.ma".
19 theorem nle_nplus: ∀p, q, r. p ⊕ q ≍ r → q ≤ r.
20 intros; elim H; clear H q r; autobatch.
23 axiom nle_nplus_comp: ∀x1,x2,x3. x1 ⊕ x2 ≍ x3 → ∀y1,y2,y3. y1 ⊕ y2 ≍ y3 →
24 x1 ≤ y1 → x2 ≤ y2 → x3 ≤ y3.
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.