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Proof step 46 from proof sub-def-any (previous step)

i % 10 = 0, ∀ 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)) ⊦ j = 0, mkDecimal(i / 10, abs(j) - 1) - mkDecimal(i0, j0) = mkDecimal(i * 10 ^ abs(j0) - i0 * 10 ^ abs(j), abs(j) + abs(j0))

User applied rule apply induction

And obtained the following new goals

Proof step 47:
i % 10 = 0, ∀ 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)) ⊦ i→n(i / 10) + i→n(i0) < i→n(i) + i→n(i0), j = 0, mkDecimal(i / 10, abs(j) - 1) - mkDecimal(i0, j0) = mkDecimal(i * 10 ^ abs(j0) - i0 * 10 ^ abs(j), abs(j) + abs(j0))
Proof step 59:
mkDecimal(i / 10, abs(j) - 1) - mkDecimal(i0, j0) = mkDecimal(i / 10 * 10 ^ abs(j0) - i0 * 10 ^ abs(abs(j) - 1), abs(abs(j) - 1) + abs(j0)), i % 10 = 0, ∀ 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)) ⊦ j = 0, mkDecimal(i / 10, abs(j) - 1) - mkDecimal(i0, j0) = mkDecimal(i * 10 ^ abs(j0) - i0 * 10 ^ abs(j), abs(j) + abs(j0))

Rule argument

subst: [i1, i2, j, j0] → [i / 10, i0, abs(j) - 1, j0]

Additional information

Used terms: i / 10, i0, abs(j) - 1, j0