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Proof step 23 from proof square-ls (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [10 ^ abs(i0)] flags: rewrite

Additional information

Used simplifier rules: abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%minus-left: ⊦ ~ i * j = ~(i * j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%neg-07: ⊦ i < ~ j ↔ i + j < 0; from specification int-abs%notneg-02: ⊦ 0 < i → ¬ i ^ j < 0; from specification int-pot Used terms: 10 ^ abs(i0)