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Proof step 24 from proof test-divides-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i

Rule argument

spec: decimal inst: name: intvalue-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i subst: [j, i] → [abs(i0), 3 * i] flags: rewrite

Additional information

Used simplifier rules: eq-one: ⊦ i * j = 1 ↔ abs(i) = 1 ∧ i = j; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: abs(i0), 3 * i