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Proof step 29 from proof div-eq-zero-01 (previous step)

i / j = 0, 0 ≤ i, j < 0, 0 ≤ i + j ⊦

User applied rule insert elim lemma

And obtained the following new goals

Proof step 30:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0)
Proof step 31:
i / j = 0, 0 ≤ i, j < 0, 0 ≤ i + j ⊦ 0 < j ∧ 0 ≤ i

Rule argument

spec: int-div inst: name: div-elim-pospos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0) subst: [i, j, i0, j0] → [i, j, i0, j0] flags: rewrite, current

Additional information

Used simplifier rules: zero-gels: ⊦ i < 0 ∧ 0 ≤ j → ¬ j < i; from specification int-abs Used terms: i, j, i0, j0