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Proof step 53 from proof sub-def-any (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 54:
⊦ ~ mkDecimal(i, j).int = mkDecimal(~ i, j).int
Proof step 55:
∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(0) + i→n(i0) → true → mkDecimal(i1, j) - mkDecimal(i2, j0) = mkDecimal(i1 * 10 ^ abs(j0) - i2 * 10 ^ abs(j), abs(j) + abs(j0)) ⊦ j = 0, mkDecimal(mkDecimal(~ i0, j0).int, mkDecimal(i0, j0).scale) = mkDecimal(~(i0 * 10 ^ abs(j)), abs(j) + abs(j0))

Rule argument

spec: decimal inst: name: getint-neg seq: ⊦ ~ mkDecimal(i, j).int = mkDecimal(~ i, j).int subst: [j, i] → [j0, i0] flags: rewrite

Additional information

Used terms: j0, i0