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Proof step 24 from proof div-ls-same (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: 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% ⊦ i < 0 ∧ 0 ≤ j → i < j; (s)% ⊦ i + j < j ↔ i < 0; (s)% ⊦ 0 < i → (i * j < 0 ↔ j < 0); (s)% ⊦ i - j < i0 ↔ i < j + i0; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i < 1 ↔ i ≤ 0; (s)% ⊦ i < j → (j ≤ i ↔ false); (as)%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