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Proof step 52 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 (mkDecimal(0, 0).int * 10 ^ mkDecimal(i0, j0).scale - mkDecimal(i0, j0).int * 10 ^ mkDecimal(0, 0).scale, mkDecimal(0, 0).scale + mkDecimal(i0, j0).scale) = mkDecimal(~(i0 * 10 ^ abs(j)), abs(j) + abs(j0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-zero: ⊦ i + 0 = i; from specification int-basic2%neg-06: ⊦ 0 - i = ~ i; from specification int-abs%one: ⊦ 1 * i = i; from specification int-mult%scale-zero: ⊦ mkDecimal(0, j).scale = 0; from specification decimal%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%intvalue-zero: ⊦ mkDecimal(0, j).int = 0; from specification decimal