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Proof step 8 from proof zero-gr (previous step)

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

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> 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]

Additional information

Used simplifier rules: ⊦ 0 < j → abs(j) = j; (s)% ⊦ i ≤ j → (j < i ↔ false); (as)% ⊦ i < j + 1 ↔ i ≤ j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ ¬ i < i; (s) Used terms: i, i + 1, j