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Proof step 7 from proof div-zero-02 (previous step)

i + j < 0, j < 0, 0 ≤ i ⊦ i / j = 0

User applied rule insert lemma

And obtained the following new goals

Proof step 8:
0 < j, 0 ≤ i, i < j ⊦ i / j = 0
Proof step 9:
i / ~ j = 0, i + j < 0, j < 0, 0 ≤ i ⊦ i / j = 0

Rule argument

spec: int-div inst: name: div-zero seq: 0 < j, 0 ≤ i, i < j ⊦ i / j = 0 subst: [j, i] → [~ j, i] flags: current, []

Additional information

Used simplifier rules: neg: ⊦ 0 < ~ i ↔ i < 0; from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs Used terms: ~ j, i