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Proof step 2 from proof longin-mult-mod (previous step)

j ∈bint, i ∈bint ⊦ j0 = 0, ((i * j) % j0)∈long

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i ∈long ∧ j ≠ 0 → (i % j)∈long

Rule argument

spec: inst: name: longin-mod seq: ⊦ i ∈long ∧ j ≠ 0 → (i % j)∈long subst: [j, i] → [j0, i * j] flags: rewrite, current

Additional information

Used simplifier rules: longin-mult-01: ⊦ i ∈bint ∧ j ∈bint → (i * j)∈long;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j0, i * j