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Proof step 44 from proof pot-root-est (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs Used terms: sqrt(2 * i)