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Proof step 48 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(0, abs(j) - 1) - mkDecimal(i0, j0) = mkDecimal(~(i0 * 10 ^ abs(j)), abs(j) + abs(j0))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 49:
⊦ mkDecimal(0, j) = mkDecimal(0, 0)
Proof step 50:
∀ 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(0, 0) - mkDecimal(i0, j0) = mkDecimal(~(i0 * 10 ^ abs(j)), abs(j) + abs(j0))

Rule argument

spec: decimal inst: name: mkDecimal-zero seq: ⊦ mkDecimal(0, j) = mkDecimal(0, 0) subst: [j] → [abs(j) - 1] flags: rewrite

Additional information

Used terms: abs(j) - 1