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Proof step 11 from proof mod-neq (previous step)

i % j = j ⊦ j = 0, j < 0 ∧ 0 ≤ i, 0 < j ∧ i < 0, j < 0 ∧ i < 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
⊦ 0 < j ∧ 0 ≤ i → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0)
Proof step 13:
i % j = j ⊦ 0 < j ∧ 0 ≤ i, j = 0, j < 0 ∧ 0 ≤ i, 0 < j ∧ i < 0, j < 0 ∧ i < 0

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-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%irref: ⊦ ¬ i < i; from specification int-basic1 Used terms: i, j, i0, j0