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Proof step 12 from proof short-larger (previous step)

i % 65536 < (i - 65536) % 65536, 0 < (i - 65536) % 65536, 65536 ≤ i, i % 65536 ≤ 32767, 0 ≤ i, 0 < i, 32768 ≤ i, 32767 < (i - 65536) % 65536 ⊦ (i - 65536) % 65536 = i % 65536 + 65536

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i, 65536, i0] rotate: T spec: int-abs inst: name: elim-sub

Additional information

Used simplifier rules: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i ∧ 0 ≤ j → (i + j) % i = j % i;% ⊦ i = i + j ↔ j = 0;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i, 65536, i0