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

sqrt(j) < sqrt(i), j < sqrt(i) ^2, i < sqrt(i) ^2, 0 < sqrt(i) ^2, i ≤ j, 0 ≤ i, 0 ≤ j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i ^2 = i * i
Proof step 8:
0 < sqrt(i) * sqrt(i), i < sqrt(i) * sqrt(i), j < sqrt(i) * sqrt(i), sqrt(j) < sqrt(i), 0 ≤ j, 0 ≤ i, i ≤ j ⊦

Rule argument

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

Additional information

Used terms: sqrt(i)