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Proof step 55 from proof pot-root-est (previous step)

2 * i = sqrt(2 * i) * sqrt(2 * i) + j0, (sqrt(2 * i) + 1) ^ 2 < 0, 0 < sqrt(2 * i), 2 * i < (sqrt(2 * i) + 1) ^ 2, 0 < i, 0 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 1024 ≤ i, j0 ≤ 2 * sqrt(2 * i), 0 ≤ sqrt(2 * i), 0 ≤ j0, ((sqrt(2 * i) + 1) ^ 2) ^ sqrt(2 * i) ≤ (2 * i) ^ sqrt(2 * i) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: pot-square-04 seq: ⊦ i ^ 2 = i * i subst: [i] → [sqrt(2 * i) + 1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ¬ i * i < 0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: sqrt(2 * i) + 1