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Proof step 13 from proof pot-square-est-div6 (previous step)

0 < i, 0 ≤ 2, 0 ≤ i / 6, 36 ≤ i, (2 ^ (i / 6)) ^ 2 ≤ (i + 1) ^ 2, 0 ≤ i ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i ^ j ≤ i0 ^ j ↔ i ≤ i0)
Proof step 15:
0 < i, 0 < 2, 0 ≤ i, 2 ^ (i / 6) ≤ i + 1, 36 ≤ i, 0 ≤ i / 6, 0 ≤ 2, 0 ≤ 2 ^ (i / 6), 0 ≤ i + 1 ⊦

Rule argument

spec: <toplevel> name: le-pos-01 seq: ⊦ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 < j → (i ^ j ≤ i0 ^ j ↔ i ≤ i0) subst: [i0, j, i] → [i + 1, 2, 2 ^ (i / 6)] flags: <all paths>

Additional information

Used simplifier rules: two-lsz: ⊦ ¬ 2 ^ i < 0;% ⊦ 0 < j ∧ 0 ≤ i → 0 ≤ i / j; (s)% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0; (s)%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i ≤ j ↔ ¬ j < i; (ss) Used terms: i + 1, 2, 2 ^ (i / 6)