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Proof step 7 from proof square-sqrt-02 (previous step)

dec.scale % 2 = 0, j * j = dec.int ⊦ mkDecimal(abs(j), dec.scale / 2) * mkDecimal(abs(j), dec.scale / 2) = dec

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))
Proof step 9:
dec.scale % 2 = 0, j * j = dec.int ⊦ mkDecimal(abs(j) * abs(j), abs(dec.scale / 2) + abs(dec.scale / 2)) = dec

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] → [dec.scale / 2, abs(j), dec.scale / 2, abs(j)] flags: rewrite, current

Additional information

Used terms: dec.scale / 2, abs(j), dec.scale / 2, abs(j)