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Proof step 9 from proof le-2pot-succ (previous step)

2 ^ i = j * 2 ^ i0 + 1, j * 2 ^ i0 < 2 ^ i, 0 < i, 0 < i0, 0 < j ⊦ 2 ^ (i - 1) * 2 + 0 = (j * 2 ^ (i0 - 1)) * 2 + 1 ∧ 0 ≤ 0 ∧ 0 < 2 ∧ 0 ≤ 1 ∧ 1 < 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
2 ^ i = j * 2 ^ i0 + 1, j * 2 ^ i0 < 2 ^ i, 0 < i, 0 < i0, 0 < j ⊦ 2 ^ (i - 1) * 2 = (j * 2 ^ (i0 - 1)) * 2 + 1

Rule argument

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-zero: ⊦ i + 0 = i; from specification int-basic2