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Proof step 4 from proof div-div-rec (previous step)

j < 0, 0 < i ⊦ ((j + 1 - 2 ^ i) / 2 ^ i - 1) / 2 = (j + 1 - 2 ^ (i + 1)) / 2 ^ (i + 1), 0 < 2 ^ i ∧ j + 1 - 2 ^ i < 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
j < 0, 0 < i, 0 ≤ i, 2 ^ i ≤ j + 1 ⊦ ((j + 1 - 2 ^ i) / 2 ^ i - 1) / 2 = (j + 1 - 2 ^ (i + 1)) / 2 ^ (i + 1)

Rule argument

Additional information

Used simplifier rules: pot2-pos: ⊦ 0 < 2 ^ i ↔ 0 ≤ i;% ⊦ i < j ↔ ¬ j ≤ i; (ss)% ⊦ i < j → ¬ j < i; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i + 0 = i; (s)% ⊦ i - j < i0 ↔ i < j + i0; (s)