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Proof step 30 from proof test-divides-01 (previous step)

(3 * i) % 10 = 0, mkDecimal((3 * i) / 10, abs(i0) - 1) = mkDecimal(1, 0), ∀ i1, i0. i→n(i1) < i→n(i) → mkDecimal(3 * i1, abs(i0)) = mkDecimal(1, 0) → false ⊦ (3 * i) / 10 = 3 * i / 10, i0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 31:
⊦ i0 % j ≠ 0 ∧ gcd(i, j) = 1 ∧ j ≠ 0 → (i * i0) % j ≠ 0
Proof step 32:
¬(i % 10 ≠ 0 ∧ gcd(3, 10) = 1 ∧ 10 ≠ 0), (3 * i) % 10 = 0, mkDecimal((3 * i) / 10, abs(i0) - 1) = mkDecimal(1, 0), ∀ i1, i0. i→n(i1) < i→n(i) → mkDecimal(3 * i1, abs(i0)) = mkDecimal(1, 0) → false ⊦ (3 * i) / 10 = 3 * i / 10, i0 = 0

Rule argument

spec: int-gcd inst: name: coprime-mod-zero seq: ⊦ i0 % j ≠ 0 ∧ gcd(i, j) = 1 ∧ j ≠ 0 → (i * i0) % j ≠ 0 subst: [j, i0, i] → [10, i, 3] flags: rewrite

Additional information

Used terms: 10, i, 3