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Proof step 6 from proof le-2pot-succ (previous step)

2 ^ i ≤ j * 2 ^ i0 + 1, 0 < i, 0 < i0, 0 < j ⊦ ¬ j * 2 ^ i0 < 2 ^ i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
2 ^ i = j * 2 ^ i0 + 1, j * 2 ^ i0 < 2 ^ i, 0 < i, 0 < i0, 0 < j ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%les: ⊦ i < j → (j ≤ i + 1 ↔ j = i + 1); from specification int-abs