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Proof step 5 from proof short-in (previous step)

0 < i % 65536, i < i % 65536, 32767 < i % 65536, 0 ≤ i, i ≤ 32767 ⊦ i % 65536 = i + 65536

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
0 < j, 0 ≤ i, i < j ⊦ i % j = i

Rule argument

seq: 0 < j, 0 ≤ i, i < j ⊦ i % j = i subst: [j, i] → [65536, i] rotate: F spec: int-div inst: name: mod-zero-03

Additional information

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