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Proof step 16 from proof band-011x-is-unsigned-fix (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ ¬ j < 0 → abs(j) = j
Proof step 18:
¬ ¬ j < 0, 1 + i→n(i) - 2 = i→n(i) - 1, # int2bits(j) < # int2bits(abs(j)), i→n(i) < # int2bits(abs(j)), 0 < i, # int2bits(j) < i→n(i), # int2bits(j) + 1 < # int2bits(abs(j)) ⊦ j = 0, abs(j) = 2 ^ n→i(i→n(i) - 1), i = 0, band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j)))

Rule argument

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

Additional information

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