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Proof step 21 from proof cong-crt-01 (previous step)

i ^ i0 = j * i2 + i, j0 * i1 = j * i2, prime(j), prime(j0), 0 < i, 0 ≤ i0 ⊦ j = j0, j * j0 | j * i2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-gcd inst: name: div-mult-01 seq: ⊦ i ≠ 0 → (i * i0 | i * i1 ↔ i0 | i1) subst: [i1, i0, i] → [i2, j0, j] flags: rewrite

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 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%ax-04: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%zero-eq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; from specification int-mult%prime-not-neg-01: ⊦ j ≤ 0 → ¬ prime(j); from specification int-gcd Used terms: i2, j0, j