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Proof step 7 from proof zero-gr (previous step)

0 < i, 0 < j, i * j ≤ 0, i * j < j, i * j < i ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: noeth-zero-ls seq: abs(i) < i0, 0 < abs(i), 0 < j ⊦ 0 < abs(i) * j subst: [i, i0, j] → [i, i + 1, j] flags: current, []

Additional information

Used simplifier rules: abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%ler: ⊦ i ≤ i; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i, i + 1, j