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Proof step 18 from proof test-divides-01 (previous step)

mkDecimal(3 * i, abs(i0)).scale = mkDecimal(1, 0).scale, mkDecimal(3 * i, abs(i0)).int = mkDecimal(1, 0).int, ∀ 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 19:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i
Proof step 20:
¬(1 % 10 = 0 ∧ 0 ≠ 0 ∧ 1 ≠ 0), mkDecimal(3 * i, abs(i0)).scale = mkDecimal(1, 0).scale, mkDecimal(3 * i, abs(i0)).int = 1, ∀ i1, i0. i→n(i1) < i→n(i) → mkDecimal(3 * i1, abs(i0)) = mkDecimal(1, 0) → false ⊦ i0 = 0, (3 * i) % 10 = 0

Rule argument

spec: decimal inst: name: intvalue-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i subst: [j, i] → [0, 1] flags: rewrite

Additional information

Used terms: 0, 1