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Proof step 16 from proof bint-mod (previous step)

2147483647 < i % j, ~2147483648 ≤ j, j ≤ 2147483647, 0 < i % j, j < i % j ⊦ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
j ≠ 0 ⊦ abs(j) ≤ i0 + 1 → ¬ i0 < i % j
Proof step 18:
¬(j ≠ 0 ∧ abs(j) ≤ 2147483647 + 1), 2147483647 < i % j, ~2147483648 ≤ j, j ≤ 2147483647, 0 < i % j, j < i % j ⊦ j = 0

Rule argument

spec: int-div inst: name: mod-nls-06 seq: j ≠ 0 ⊦ abs(j) ≤ i0 + 1 → ¬ i0 < i % j subst: [j, i, i0] → [j, i, 2147483647] flags: rewrite

Additional information

Used terms: j, i, 2147483647