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Proof step 23 from proof div-ls-same (previous step)

j0 < j, 0 < j, i0 * j + j0 < i0, 0 ≤ j0, 0 ≤ i0, 0 < i0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: ls-same-06 seq: ⊦ i + j * j0 < j ↔ i + j * (j0 - 1) < 0 subst: [i, j0, j] → [j0, j, i0] flags: rewrite

Additional information

Used simplifier rules: lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%zero-ls: ⊦ 0 < i → (i * j < 0 ↔ j < 0); from specification int-mult%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%lsone: ⊦ i < 1 ↔ i ≤ 0; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j0, j, i0