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Proof step 10 from proof sqrt-exact-def (previous step)

dec.scale % 2 = 0, isSquare(dec.int), even(dec.scale) ⊦ mkDecimal(sqrt(dec.int * 10 ^ (2 * abs(i))), dec.scale / 2 + abs(i)) = mkDecimal(sqrt(dec.int), dec.scale / 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ isSquare(i) ∧ isSquare(j) → sqrt(i * j) = sqrt(i) * sqrt(j)
Proof step 12:
isSquare(dec.int) ∧ isSquare(10 ^ (2 * abs(i))), dec.scale % 2 = 0, isSquare(dec.int), even(dec.scale) ⊦ mkDecimal(sqrt(dec.int) * sqrt(10 ^ (2 * abs(i))), dec.scale / 2 + abs(i)) = mkDecimal(sqrt(dec.int), dec.scale / 2)

Rule argument

spec: int-square inst: name: sqrt-mult-squares seq: ⊦ isSquare(i) ∧ isSquare(j) → sqrt(i * j) = sqrt(i) * sqrt(j) subst: [j, i] → [10 ^ (2 * abs(i)), dec.int] flags: rewrite

Additional information

Used simplifier rules: isSquare-10pot: ⊦ isSquare(10 ^ (2 * abs(i))); from specification int-pot%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 10 ^ (2 * abs(i)), dec.int