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Proof step 11 from proof square-ls (previous step)

⊦ mkDecimal(i * i, 2 * abs(i0)) < mkDecimal(i1 * i1, 2 * abs(i2)) ↔ abs(mkDecimal(i, i0)) < abs(mkDecimal(i1, i2))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ mkDecimal(i, j) < mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) < i0 * 10 ^ abs(j)
Proof step 13:
⊦ (i * i) * 10 ^ abs(2 * abs(i2)) < (i1 * i1) * 10 ^ abs(2 * abs(i0)) ↔ abs(mkDecimal(i, i0)) < abs(mkDecimal(i1, i2))

Rule argument

spec: inst: name: less-def-any seq: ⊦ mkDecimal(i, j) < mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) < i0 * 10 ^ abs(j) subst: [j0, i0, j, i] → [2 * abs(i2), i1 * i1, 2 * abs(i0), i * i] flags: rewrite, current

Additional information

Used terms: 2 * abs(i2), i1 * i1, 2 * abs(i0), i * i