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Proof step 45 from proof pot-root-est (previous step)

2 * i = j * j + j0, j = sqrt(2 * i), (2 * i) ^ j < ((j + 1) ^ 2) ^ j, 0 < i, 2 * i < (j + 1) ^ 2, (j ^ 2 / 2) / 3 ≤ i / 3, j ^ 2 / 2 ≤ i, 0 ≤ j0, 0 ≤ j, j0 ≤ 2 * j, 1024 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ i, j ^ 2 ≤ 2 * i ⊦ j * j / 6 ≤ (j ^ 2 / 2) / 3

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] → [j] flags: <all paths>

Additional information

Used simplifier rules: j ≠ 0, j0 ≠ 0 ⊦ (i / (* j)) / (* j0) = i / (j * j0); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → i * i0 / j ≤ (i * i0) / j; (s) Used terms: j