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Proof step 19 from proof int2int-neg (previous step)

0 = 2 ^ (i + 1) + j, n→i(# int2bits(~ j)) = i + 1, 2 + j < 2 ^ i, 0 < 2 ^ i + j, j + 1 < 2 ^ (i + 1), 0 ≤ 2 ^ i, 2 ^ (i + 1) < 2 ^ i, j < 2 ^ i, 0 < 2 ^ (i + 1), 1 < 2 ^ i, 0 < 2 ^ i, j < 2 ^ (i + 1), j < 0 ⊦ j = bits2int([])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j

Rule argument

seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [i, 2] rotate: F spec: int-pot inst: name: succ

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i ^ j ↔ i = 1 ∨ 0 ≤ j);% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ 0 < i → (i * j < i ↔ j < 1);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: i, 2