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Proof step 10 from proof modlep-03 (previous step)

i1 = i2 + j, 0 ≤ i1 + j1, abs(j1) < abs(i1), i1 + j1 < abs(i1), j * i + i1 ≤ j * i0, 0 < j, j ≤ abs(i1), i0 < i, abs(j1) < j, i1 + j1 < j ⊦ i1 = 0, j * (i + 1) + i1 ≤ j + j * i0 ∧ abs(i2) < j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: ls-add-03: ⊦ i * j + i0 < i * (j + j1) + j0 ↔ i0 < i * j1 + j0;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%irref: ⊦ ¬ i < i; from specification int-basic1%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs%add-less: ⊦ 0 < i → i1 < i1 + i; from specification int-basic2%ls-01: ⊦ i + j < i + i0 ↔ j < i0; from specification int-basic2%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%lep-02: ⊦ i + j ≤ i + j0 ↔ j ≤ j0; 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%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2