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Proof step 19 from proof dec2int-def-any (previous step)

10 ≠ 0, ∃ j0. i = j0 * 10, dec2int(mkDecimal(i / 10, abs(j) - 1)) = (i / 10) / 10 ^ (abs(j) - 1), ∀ i0, j. i→n(i0) < i→n(i) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ j = 0, (i / 10) / 10 ^ (abs(j) - 1) = i / 10 ^ abs(j)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 20:
dec2int(mkDecimal(j0, abs(j) - 1)) = j0 / 10 ^ (abs(j) - 1), ∀ i0, j. i→n(i0) < i→n(j0 * 10) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ j = 0, j0 / 10 ^ (abs(j) - 1) = (j0 * 10) / 10 ^ abs(j)

Rule argument

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%one: ⊦ 1 * i = i; from specification int-mult%div-mult-num: j ≠ 0, j0 % j = 0 ⊦ (i * (* j0)) / (* j) = i * j0 / j; from specification int-div