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Proof step 15 from proof test-divides-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ dec_i = dec_j ↔ dec_i.int = dec_j.int ∧ dec_i.scale = dec_j.scale
Proof step 17:
mkDecimal(3 * i, abs(i0)).int = mkDecimal(1, 0).int ∧ mkDecimal(3 * i, abs(i0)).scale = mkDecimal(1, 0).scale, ∀ i1, i0. i→n(i1) < i→n(i) → mkDecimal(3 * i1, abs(i0)) = mkDecimal(1, 0) → false ⊦ (3 * i) % 10 = 0, i0 = 0

Rule argument

spec: decimal inst: name: Equality seq: ⊦ dec_i = dec_j ↔ dec_i.int = dec_j.int ∧ dec_i.scale = dec_j.scale subst: [dec_j, dec_i] → [mkDecimal(1, 0), mkDecimal(3 * i, abs(i0))] flags: rewrite

Additional information

Used terms: mkDecimal(1, 0), mkDecimal(3 * i, abs(i0))