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Proof step 11 from proof div-add-nosucc (previous step)

j0 * j + j = i0 + 1, i0 / j = i1 / j + j0, j = i1 + 1, 1 < j, 0 < j, 0 ≤ j0 ⊦ i0 / j = j0, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
(j0 * (i1 + 1) + i1) / (i1 + 1) = i1 / (i1 + 1) + j0, 0 < i1, 0 ≤ j0, 0 ≤ i1 ⊦ i1 / (i1 + 1) = 0, ~1 = i1

Rule argument

Additional information

Used simplifier rules: ⊦ i = i + j ↔ j = 0; (s)%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs% ⊦ ~1 < i ↔ 0 ≤ i; (s)% ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; (s)% ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + j = i + i0 ↔ j = i0; (s)