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Proof step 8 from proof square-ls (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))
Proof step 10:
⊦ mkDecimal(i * i, 2 * abs(i0)) < mkDecimal(i1 * i1, abs(i2) + abs(i2)) ↔ abs(mkDecimal(i, i0)) < abs(mkDecimal(i1, i2))

Rule argument

spec: inst: name: mult-def-any seq: ⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0)) subst: [j0, i0, j, i] → [i2, i1, i2, i1] flags: rewrite, current

Additional information

Used terms: i2, i1, i2, i1