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Proof step 9 from proof modlsp-03 (previous step)

i0 < i, 0 < j, j * i + i1 + j1 - j1 < j * i0, abs(j1) < j, i1 + j1 < j, j * i + i1 < j * i0, abs(j1) < abs(i1), i1 + j1 < abs(i1), j ≤ abs(i1), 0 ≤ i1 + j1 ⊦ i1 = 0, j * (i + 1) + (i1 - j) < j * i0 ∧ abs(i1 - j) < j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: dist-rsplit: ⊦ i * (j + j0) = i * j + i * j0;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;% ⊦ i + 0 = i; (s)% ⊦ i - j = i0 ↔ i = i0 + j; (s)% ⊦ 0 < abs(i) ↔ i ≠ 0; (s)%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i + (j - i) = j; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2