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Proof step 16 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) * 10 ^ abs(i), abs(dec.scale) / 2 + abs(i))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [dec.scale] flags: rewrite

Additional information

Used simplifier rules: abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j); from specification int-div%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%scale-not-neg: ⊦ ¬ dec.scale < 0; from specification decimal Used terms: dec.scale