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Proof step 1 from proof square-sqrt-01 (conclusion)

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

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
⊦ mkDecimal(0, 0) ≤ dec → mkDecimal(sqrt((dec * dec).int), (dec * dec).scale / 2) = dec
Proof step 3:
mkDecimal(0, 0) ≤ abs(dec) → mkDecimal(sqrt((abs(dec) * abs(dec)).int), (abs(dec) * abs(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: square-sqrt seq: ⊦ mkDecimal(0, 0) ≤ dec → mkDecimal(sqrt((dec * dec).int), (dec * dec).scale / 2) = dec subst: [dec] → [abs(dec)] flags: current, []

Additional information

Used terms: abs(dec)