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Proof step 14 from proof sub-def-any (previous step)

∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(i0) → true → mkDecimal(i1, j) - mkDecimal(i2, j0) = mkDecimal(i1 * 10 ^ abs(j0) - i2 * 10 ^ abs(j), abs(j) + abs(j0)) ⊦ mkDecimal(i * 10 ^ mkDecimal(i0, j0).scale - mkDecimal(i0, j0).int * 10 ^ mkDecimal(i, j).scale, mkDecimal(i, j).scale + mkDecimal(i0, j0).scale) = mkDecimal(i * 10 ^ abs(j0) - i0 * 10 ^ abs(j), abs(j) + abs(j0)), i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0, i % 10 = 0 ∧ j ≠ 0, i0 % 10 = 0 ∧ j0 ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: decimal inst: name: scale-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j) subst: [j, i] → [j0, i0] flags: rewrite

Additional information

Used terms: j0, i0