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Proof step 23 from proof div-eq-zero-01 (previous step)

i0 * j + j0 < i0, j < j0, j < 0, j ≤ i0 * j + j0, j < i0 * j + j0, j < ~1, 0 < i0, j0 < i0, j0 ≤ 0, j < i0, (i0 * j + j0) + 1 < i0 ⊦ i0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ j ≤ (* i1) * j + i ↔ 0 ≤ (i1 - 1) * j + i
Proof step 25:
i0 * j + j0 < i0, j < j0, j < 0, 0 ≤ (i0 - 1) * j + j0, j < i0 * j + j0, j < ~1, 0 < i0, j0 < i0, j0 ≤ 0, j < i0, (i0 * j + j0) + 1 < i0 ⊦ i0 = 0

Rule argument

spec: int-mult inst: name: numle-12 seq: ⊦ j ≤ (* i1) * j + i ↔ 0 ≤ (i1 - 1) * j + i subst: [i, i1, j] → [j0, i0, j] flags: rewrite

Additional information

Used terms: j0, i0, j