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Proof step 4 from proof square-sqrt (previous step)

0 ≤ i ⊦ mkDecimal(sqrt((mkDecimal(i, i0) * mkDecimal(i, i0)).int), (mkDecimal(i, i0) * mkDecimal(i, i0)).scale / 2) = mkDecimal(i, i0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0))
Proof step 6:
0 ≤ i ⊦ mkDecimal(sqrt(mkDecimal(i * i, abs(i0) + abs(i0)).int), mkDecimal(i * i, abs(i0) + abs(i0)).scale / 2) = mkDecimal(i, i0)

Rule argument

spec: inst: name: mult-def-any seq: ⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0)) subst: [j0, i0, j, i] → [i0, i, i0, i] flags: rewrite, current

Additional information

Used terms: i0, i, i0, i