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

i ≤ j, sqrt(j) < sqrt(i), 0 ≤ i, 0 ≤ j, j < sqrt(i) ^2, i < sqrt(i) ^2, 0 < sqrt(i) ^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-nls: ⊦ 0 ≤ i → ¬ i < sqrt(i) * sqrt(i);%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: sqrt(i)