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Proof step 2 from proof sqrt-exact-square (previous step)

mkDecimal(0, 0) ≤ dec0 ⊦ sqrt(dec0 * dec0, i) = dec0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ isSquare(dec) → sqrt(dec, i) = mkDecimal(sqrt(dec.int), dec.scale / 2)
Proof step 4:
isSquare(dec0 * dec0), mkDecimal(0, 0) ≤ dec0 ⊦ mkDecimal(sqrt((dec0 * dec0).int), (dec0 * dec0).scale / 2) = dec0

Rule argument

spec: inst: name: sqrt-exact-def seq: ⊦ isSquare(dec) → sqrt(dec, i) = mkDecimal(sqrt(dec.int), dec.scale / 2) subst: [i, dec] → [i, dec0 * dec0] flags: rewrite, current

Additional information

Used simplifier rules: isSquare-square: ⊦ isSquare(dec * dec);%mult-a: ⊦ dec0 * dec1 * dec2 = (dec0 * dec1) * dec2; from specification decimal-simple-ops%mult-c: ⊦ dec_i * dec_j = dec_j * dec_i; from specification decimal-simple-ops Used terms: i, dec0 * dec0