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Proof step 14 from proof dec2int-def-any (previous step)

i % 10 = 0, ∀ i0, j. i→n(i0) < i→n(i) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ j = 0, dec2int(mkDecimal(i / 10, abs(j) - 1)) = i / 10 ^ abs(j)

User applied rule apply induction

And obtained the following new goals

Proof step 15:
i % 10 = 0, ∀ i0, j. i→n(i0) < i→n(i) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ i→n(i / 10) < i→n(i), j = 0, dec2int(mkDecimal(i / 10, abs(j) - 1)) = i / 10 ^ abs(j)
Proof step 16:
dec2int(mkDecimal(i / 10, abs(j) - 1)) = (i / 10) / 10 ^ abs(abs(j) - 1), i % 10 = 0, ∀ i0, j. i→n(i0) < i→n(i) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ j = 0, dec2int(mkDecimal(i / 10, abs(j) - 1)) = i / 10 ^ abs(j)

Rule argument

subst: [i0, j] → [i / 10, abs(j) - 1]

Additional information

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