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Proof step 16 from proof int2bits-len-range (previous step)

0 ≤ 2 ^ i + j, 0 ≤ i0, 2 ^ i0 + j ≤ 0, 0 < 2 ^ i0 * 2 + j, j < 2 ^ i0, j < i, j + 1 < 2 ^ i, j < 2 ^ i, 2 ^ i0 + j ≤ i, 0 ≤ i, 2 ^ i0 + j < 2 ^ i, j + 1 < 2 ^ i0, 0 < 2 ^ i, j < i0, i0 ≤ i, 2 ^ i0 + j ≤ i0, j < 0, 0 < 2 ^ i0, i→n(i) + 1 < # int2bits(j) ⊦ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ i < 0 → # int2bits(i) = # int2bits(~ i - 1)
Proof step 18:
j < 0, 0 ≤ 2 ^ i + j, 0 ≤ i0, 2 ^ i0 + j ≤ 0, 0 < 2 ^ i0 * 2 + j, j < 2 ^ i0, j < i, j + 1 < 2 ^ i, j < 2 ^ i, 2 ^ i0 + j ≤ i, 0 ≤ i, 2 ^ i0 + j < 2 ^ i, j + 1 < 2 ^ i0, 0 < 2 ^ i, j < i0, i0 ≤ i, 2 ^ i0 + j ≤ i0, j < 0, 0 < 2 ^ i0, i→n(i) + 1 < # int2bits(~ j - 1) ⊦ j = 0

Rule argument

name: int2bits-len-neg-01 rotate: F subst: [i] → [j]

Additional information

Used terms: j