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Proof step 46 from proof pot-root-est (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: ls-pos-03 seq: ⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i ^ j < i0 ^ j ↔ i < i0) subst: [i0, j, i] → [(j + 1) ^ 2, j, 2 * i] flags: rewrite, current

Additional information

Used simplifier rules: lels: ⊦ ¬ 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%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%modzero: ⊦ 0 < i ∧ abs(j0) < j → ¬ i * j + j0 < 0; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%square-not-neg-03: ⊦ 0 < i → ¬ sqrt(2 * i) ≤ 0; from specification int-square Used terms: (j + 1) ^ 2, j, 2 * i