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Proof step 7 from proof div-add-succ (previous step)

0 < j, 1 < j, 0 < i, 0 ≤ j ⊦ i % j = 0, (i - 1) / j = i / j

User applied rule insert elim lemma

And obtained the following new goals

Proof step 8:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0)
Proof step 9:
i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0 ∧ 0 ≤ i, 0 < j, 1 < j, 0 < i, 0 ≤ j ⊦ j0 = 0, (i - 1) / j = i0

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: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: i, j, i0, j0