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Proof step 1 from proof mod-twoodd (conclusion)

0 ≤ i, 0 < j ⊦ (2 * i + 1) % (2 * j) = i % j * 2 + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
j ≠ 0 ⊦ i % j = i - i / j * j
Proof step 3:
2 * j ≠ 0, 0 ≤ i, 0 < j ⊦ 2 * i + 1 - (2 * i + 1) / (2 * j) * 2 * j = i % j * 2 + 1

Rule argument

spec: int-div inst: name: mod-rew seq: j ≠ 0 ⊦ i % j = i - i / j * j subst: [j, i] → [2 * j, 2 * i + 1] flags: rewrite, current

Additional information

Used simplifier rules: two-zero: ⊦ 2 * i = 0 ↔ i = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lf-03: ⊦ i < j ∧ i = i0 → i0 < j; (forward) from specification int-basic1%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1 Used terms: 2 * j, 2 * i + 1