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Proof step 14 from proof twopot-mone-div (previous step)

(2 * 2 ^ (i - 1)) / (2 * 2 ^ j -1) = 2 ^ (i - 1) / 2 ^ j -1, 0 < j, j ≤ i, 0 ≤ i, 0 ≤ j, 0 < i, ∀ i0, j. i→n(i0) < i→n(i) → true → j ≤ i0 ∧ 0 ≤ j → (2 ^ i0 - 1) / 2 ^ j = 2 ^ i0 / 2 ^ j - 1 ⊦ (2 ^ (i - 1) * 2) / (2 * 2 ^ j -1) = (2 ^ (i - 1) * 2 - 1) / (2 * 2 ^ j -1) + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
(2 * 2 ^ (i - 1)) / (2 * 2 ^ (j - 1)) = 2 ^ (i - 1) / 2 ^ (j - 1), j ≤ i, 0 ≤ i, 0 ≤ j, 0 < i, 0 < j, ∀ i0, j. i→n(i0) < i→n(i) → true → j ≤ i0 ∧ 0 ≤ j → (2 ^ i0 - 1) / 2 ^ j = 2 ^ i0 / 2 ^ j - 1 ⊦ 2 ^ (i - 1) / 2 ^ (j - 1) = (2 ^ (i - 1) * 2 - 1) / (2 * 2 ^ (j - 1)) + 1

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%sub-pred: ⊦ i -1 = i - 1; from specification int-abs