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Proof step 11 from proof le-2pot-succ (previous step)

i = i1 + 1, 2 ^ i = j * 2 ^ i0 + 1, j * 2 ^ i0 < 2 ^ i, 0 < i, 0 < i0, 0 < j ⊦ 2 ^ i1 * 2 = (j * 2 ^ (i0 - 1)) * 2 + 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 12:
2 ^ i1 * 2 = j * 2 ^ i0 + 1, 0 ≤ i1, 0 < i0, 0 < j, j * 2 ^ i0 < 2 ^ i1 * 2 ⊦ 2 ^ i1 * 2 = (j * 2 ^ (i0 - 1)) * 2 + 1

Rule argument

Additional information

Used simplifier rules: succ: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j;%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%mone-06: ⊦ ~1 < i ↔ 0 ≤ i; from specification int-abs%numls-02: ⊦ (* j) < i0 + (* j0) ↔ j - j0 < i0; from specification int-abs