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Proof step 7 from proof le-2pot-succ (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Proof step 8:
i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1
Proof step 9:
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

Rule argument

spec: int-mult inst: name: modeqp seq: i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [2 ^ (i - 1), 2, 0, j * 2 ^ (i0 - 1), 1] flags:

Additional information

Used terms: 2 ^ (i - 1), 2, 0, j * 2 ^ (i0 - 1), 1