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Proof step 5 from proof ls-02 (previous step)

i / i0 < j / i0, 0 < i0, j < 0, i < 0, j ≤ i ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: ls-01 seq: i0 ≠ 0, j0 ≠ 0, 0 ≤ i, 0 ≤ i0, i ≤ j, i0 ≤ j0 ⊦ i / j0 ≤ j / i0 subst: [i0, j0, i, j] → [i0, i0, ~ i, ~ j]

Additional information

Used simplifier rules: neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ ~ i ≤ j ↔ 0 ≤ i + j; (s)% ⊦ i + ~ j = 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 - i0 ↔ i + i0 ≤ j; (s)% ⊦ i + 0 = i; (s)% ⊦ i < j → (j ≤ i ↔ false); (as)% ⊦ i ≤ ~ j ↔ i + j ≤ 0; (s)% ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ i ≤ i; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s) Used terms: i0, i0, ~ i, ~ j