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Proof step 45 from proof mult-def-any (previous step)

∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(j1 * 10) + i→n(i0) → true → mkDecimal(i1, j) * mkDecimal(i2, j0) = mkDecimal(i1 * i2, abs(j) + abs(j0)) ⊦ abs(j) + abs(j0) = 0, j = 0, mkDecimal(j1, abs(j) - 1) * mkDecimal(i0, j0) = mkDecimal(j1 * i0, abs(j) + abs(j0) - 1)

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [i1, i2, j, j0] → [j1, i0, abs(j) - 1, j0]

Additional information

Used simplifier rules: abs-abs: ⊦ j ≠ 0 → abs(abs(j) - 1) = abs(j) - 1; from specification int-abs%sub-add-01: ⊦ i + (j - i0) = i + j - i0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j1, i0, abs(j) - 1, j0