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Proof step 13 from proof sqrt-exact-def (previous step)

dec.scale % 2 = 0, isSquare(dec.int), even(dec.scale) ⊦ mkDecimal(sqrt(dec.int) * 10 ^ 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 14:
⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0)
Proof step 15:
0 ≤ abs(i), dec.scale % 2 = 0, isSquare(dec.int), even(dec.scale) ⊦ mkDecimal(sqrt(dec.int) * 10 ^ abs(i), dec.scale / 2 + abs(i)) = mkDecimal(sqrt(dec.int) * 10 ^ abs(i), abs(dec.scale / 2) + abs(i))

Rule argument

spec: decimal inst: name: mkDecimal-enlarge seq: ⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0) subst: [j0, j, i] → [abs(i), dec.scale / 2, sqrt(dec.int)] flags: rewrite

Additional information

Used simplifier rules: abs-03: ⊦ 0 ≤ abs(i); from specification int-abs Used terms: abs(i), dec.scale / 2, sqrt(dec.int)