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Proof step 11 from proof square-sqrt-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ¬ j < 0 → abs(j) = j
Proof step 13:
¬ ¬ (dec * dec).int < 0, 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
Proof step 14:
¬ (dec * dec).int < 0, mkDecimal(sqrt((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: int-abs inst: name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [(dec * dec).int] flags: rewrite

Additional information

Used terms: (dec * dec).int