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Proof step 7 from proof root-elim (previous step)

0 ≤ i, sqrt(i) ^2 ≤ i, i < (sqrt(i) + 1) * (sqrt(i) + 1), sqrt(i) ^2 < (sqrt(i) + 1) * (sqrt(i) + 1), 0 < (sqrt(i) + 1) * (sqrt(i) + 1) ⊦ ∃ j0. i = sqrt(i) * sqrt(i) + j0 ∧ j0 ≤ 2 * sqrt(i) ∧ 0 ≤ sqrt(i) ∧ 0 ≤ j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ i ^2 = i * i
Proof step 9:
0 ≤ i, sqrt(i) * sqrt(i) ≤ i, i < (sqrt(i) + 1) * (sqrt(i) + 1), sqrt(i) * sqrt(i) < (sqrt(i) + 1) * (sqrt(i) + 1), 0 < (sqrt(i) + 1) * (sqrt(i) + 1) ⊦ ∃ j0. i = sqrt(i) * sqrt(i) + j0 ∧ j0 ≤ 2 * sqrt(i) ∧ 0 ≤ sqrt(i) ∧ 0 ≤ j0

Rule argument

spec: inst: name: Square-def seq: ⊦ i ^2 = i * i subst: [i] → [sqrt(i)] flags: rewrite, current

Additional information

Used terms: sqrt(i)