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Proof step 3 from proof lsf-02 (previous step)

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

User applied rule insert lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);% ⊦ i ≤ j → ¬ j < i; (s)% ⊦ i ≤ ~ j ↔ i + j ≤ 0; (s)% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ ~ j < ~ i ↔ i < j; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s) Used terms: ~ i, i0, j