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Proof step 16 from proof ushort-short (previous step)

32767 < (s2i(sho) + 65536) % 65536, s2i(sho) < 0, 0 < (s2i(sho) + 65536) % 65536, 65536 ≤ abs(s2i(sho) + 65536), ~65536 < s2i(sho) ⊦ (s2i(sho) + 65536) % 65536 = s2i(sho) + 65536, ~65536 = s2i(sho)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [s2i(sho) + 65536] rotate: F spec: int-abs inst: name: Abs-pos

Additional information

Used simplifier rules: short-min-02: ⊦ i ≤ ~32768 → ¬ s2i(sho) < i;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i + j = j + i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i + j + i0 = (i + j) + i0; Used terms: s2i(sho) + 65536