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Proof step 19 from proof square-ls (previous step)

0 ≤ abs(i0) ⊦ i * i * 10 ^ abs(i2) * 10 ^ abs(i2) < i1 * i1 * 10 ^ abs(i0) * 10 ^ abs(i0) ↔ abs(mkDecimal(i, i0)) < abs(mkDecimal(i1, i2))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: abs-03: ⊦ 0 ≤ abs(i); from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%abs-eqall: ⊦ abs(i * j) = abs(i) * abs(j); from specification int-mult%square-ls: ⊦ i * i < j * j ↔ abs(i) < abs(j); from specification int-mult