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Proof step 10 from proof bint-mod (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ i0 - 1 ≤ ~ abs(j) ∧ j ≠ 0 → ¬ i % j < i0
Proof step 12:
¬(~2147483648 - 1 ≤ ~ abs(j) ∧ j ≠ 0), i % j < ~2147483648, ~2147483648 ≤ j, j ≤ 2147483647, i % j < j, i % j < 0 ⊦ j = 0

Rule argument

spec: int-div inst: name: mod-nls-04 seq: ⊦ i0 - 1 ≤ ~ abs(j) ∧ j ≠ 0 → ¬ i % j < i0 subst: [i0, j, i] → [~2147483648, j, i] flags: rewrite

Additional information

Used terms: ~2147483648, j, i