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Proof step 6 from proof root-nls (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i ^2 = i * i

Rule argument

spec: <toplevel> name: Square-def seq: ⊦ i ^2 = i * i subst: [i] → [sqrt(i)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ i ≤ j → ¬ j < i; (s) Used terms: sqrt(i)