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Proof step 5 from proof root-nls (previous step)

sqrt(i) ^2 < sqrt(i) * sqrt(i), i < sqrt(i) ^2 + 2 * sqrt(i) + 1 ^2, sqrt(i) ^2 ≤ i, 0 < sqrt(i) * sqrt(i), 0 ≤ i, i < sqrt(i) * sqrt(i), 0 < sqrt(i) ^2 + 2 * sqrt(i) + 1 ^2, 0 < 2 * sqrt(i) + 1 ^2 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ i ^2 = i * i

Rule argument

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

Additional information

Used simplifier rules: root-abs: ⊦ 0 ≤ i → abs(sqrt(i)) = sqrt(i);%square-ls: ⊦ i * i < j * j ↔ abs(i) < abs(j); from specification int-mult%irref: ⊦ ¬ i < i; from specification int-basic1%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: sqrt(i)