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

i ^ ~ j + 1 = 0, i ^ ~ j < i, j ≤ i ^ ~ j, j < i, j + 1 < i, i ^ ~ j < 0, 0 ≤ i, 1 / i ^ ~ j + 1 < i, 1 / i ^ ~ j < i, j < 0, 0 < i ⊦

User applied rule insert lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: notneg seq: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i ^ j < 0 subst: [i, j] → [i, ~ j] flags: current, []

Additional information

Used simplifier rules: negle-07: ⊦ i ≤ ~ j ↔ i + j ≤ 0; from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: i, ~ j