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Proof step 7 from proof diveq-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
j0 < j, 0 ≤ j0, 0 < j, 0 ≤ i0, (i0 * j + j0) / j * j ≤ i0 * j + j0, i0 * j + j0 < ((i0 * j + j0) / j + 1) * j, i0 ≤ (i0 * j + j0) / j + 1, ~1 ≤ (i0 * j + j0) / j ⊦ (i0 * j + j0) / j = i0

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%numle-02: ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs