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Proof step 2 from proof square-sqrt-02 (previous step)

dec.scale % 2 = 0, isSquare(dec.int) ⊦ mkDecimal(sqrt(dec.int), dec.scale / 2) * mkDecimal(sqrt(dec.int), dec.scale / 2) = dec

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ isSquare(i) ↔ (∃ j. j * j = i)
Proof step 4:
dec.scale % 2 = 0, ∃ j. j * j = dec.int ⊦ mkDecimal(sqrt(dec.int), dec.scale / 2) * mkDecimal(sqrt(dec.int), dec.scale / 2) = dec

Rule argument

spec: int-square inst: name: isSquare-def seq: ⊦ isSquare(i) ↔ (∃ j. j * j = i) subst: [i] → [dec.int] flags: rewrite

Additional information

Used terms: dec.int