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Proof step 10 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 = (j * 2 ^ (i0 - 1)) * 2 + 1

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
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

Rule argument

spec: int-abs inst: name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i, 1, i1] flags:

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i, 1, i1