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Proof step 14 from proof band-011x-is-unsigned-03 (previous step)

# int2bits(j) < # int2bits(abs(j)) ⊦ j = 0, abs(j) = 2 ^ n→i(# int2bits(j) - 1), band(j, 2 ^ n→i(# int2bits(j)) - 1) = bits2uint(int2bits(j))

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ j < 0 → abs(j) = 0 - j
Proof step 16:
j < 0, # int2bits(j) < # int2bits(0 - j) ⊦ j = 0, 0 - j = 2 ^ n→i(# int2bits(j) - 1), band(j, 2 ^ n→i(# int2bits(j)) - 1) = bits2uint(int2bits(j))

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [j] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used simplifier rules: ⊦ ¬ i < j → (i ≠ j ↔ j < i);% ⊦ ¬ j < 0 → abs(j) = j;% ⊦ ¬ n < n; Used terms: j