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Proof step 5 from proof mod-mult-add (previous step)

0 < j, 0 < i0, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 < i1 ∧ 0 < j → (i + i1 * j) |%| j = i |%| j ⊦ (i + i0 * j) |%| j = i |%| j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 < j → i |%| j = (i - j) |%| j
Proof step 7:
0 < j, 0 < j, 0 < i0, ∀ i1, j, i. i→n(i1) < i→n(i0) → 0 < i1 ∧ 0 < j → (i + i1 * j) |%| j = i |%| j ⊦ (i + i0 * j - j) |%| j = i |%| j

Rule argument

spec: int-mod inst: name: mod-rec-any seq: ⊦ 0 < j → i |%| j = (i - j) |%| j subst: [j, i] → [j, i + i0 * j] flags: rewrite, current

Additional information

Used terms: j, i + i0 * j