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Proof step 8 from proof div-add-nosucc (previous step)

(j * j0) % j = 0 ∧ 0 ≤ j - 1 ∧ 0 ≤ j * j0 ∧ 0 < j → ((j - 1) + j * j0) / j = (j - 1) / j + (j * j0) / j, j0 * j + j = i0 + 1, 0 < j, 1 < j, 0 ≤ j0 ⊦ j = 0, i0 / j = j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
j0 * j + j = i0 + 1, i0 / j = (j - 1) / j + j0, 0 ≤ j0, 1 < j, 0 < j ⊦ i0 / j = j0, j = 0

Rule argument

Additional information

Used simplifier rules: mod-mult-04: j ≠ 0 ⊦ (i * j) % j = 0;%div-mult-03: j ≠ 0 ⊦ (i * j) / j = i;%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%numsub: ⊦ (* i) + i0 - (* j) = (i - j) + i0; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult