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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ even(dec_i.scale) → sqrt(dec_i, i) = mkDecimal(sqrt(dec_i.int * 10 ^ (2 * abs(i))), dec_i.scale / 2 + abs(i))
Proof step 4:
¬ even(dec.scale), isSquare(dec) ⊦ sqrt(dec, i) = mkDecimal(sqrt(dec.int), dec.scale / 2)
Proof step 7:
even(dec.scale), isSquare(dec) ⊦ mkDecimal(sqrt(dec.int * 10 ^ (2 * abs(i))), dec.scale / 2 + abs(i)) = mkDecimal(sqrt(dec.int), dec.scale / 2)

Rule argument

spec: inst: name: sqrt-even-precision-def seq: ⊦ even(dec_i.scale) → sqrt(dec_i, i) = mkDecimal (sqrt(dec_i.int * 10 ^ (2 * abs(i))), dec_i.scale / 2 + abs(i)) subst: [i, dec_i] → [i, dec] flags: rewrite, current

Additional information

Used terms: i, dec