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Proof step 37 from proof pot-root-est (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: ls-03 seq: 0 < j0, 0 ≤ i, i ≤ j ⊦ i / j0 ≤ j / j0 subst: [j, j0, i] → [i, 3, j ^ 2 / 2] flags: rewrite

Additional information

Used simplifier rules: notneg: ⊦ 0 ≤ i ∧ 0 ≤ j → ¬ i ^ j < 0;%div-div-num: j ≠ 0, j0 ≠ 0 ⊦ (i / (* j)) / (* j0) = i / (j * j0); from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%num-ls: ⊦ 0 < j ∧ 0 ≤ i → (i / (* j) < j0 ↔ i < j * j0); from specification int-div%div-two-zero-01: ⊦ 0 ≤ i / 2 ↔ ~1 ≤ i; from specification int-div%numlsf: ⊦ i < (* j) ∧ j < 0 → i < 0; (forward) from specification int-basic1%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs Used terms: i, 3, j ^ 2 / 2