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Proof step 9 from proof square-sqrt-01 (previous step)

mkDecimal(sqrt(abs((dec * dec).int)), abs(dec * dec).scale / 2) = abs(dec) ⊦ mkDecimal(sqrt((dec * dec).int), (dec * dec).scale / 2) * mkDecimal(sqrt((dec * dec).int), (dec * dec).scale / 2) = dec * dec

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ abs(dec).scale = dec.scale
Proof step 11:
mkDecimal(sqrt(abs((dec * dec).int)), (dec * dec).scale / 2) = abs(dec) ⊦ mkDecimal(sqrt((dec * dec).int), (dec * dec).scale / 2) * mkDecimal(sqrt((dec * dec).int), (dec * dec).scale / 2) = dec * dec

Rule argument

spec: inst: name: scale-abs seq: ⊦ abs(dec).scale = dec.scale subst: [dec] → [dec * dec] flags: rewrite, current

Additional information

Used terms: dec * dec