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Proof step 19 from proof band-011x-is-unsigned-fix (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ ¬(∃ i. j = ~(2 ^ i)) ∧ j < 0 → # int2bits(j) = # int2bits(~ j)
Proof step 21:
¬(¬(∃ i. j = ~(2 ^ i)) ∧ j < 0), 1 + i→n(i) - 2 = i→n(i) - 1, # int2bits(j) < # int2bits(~ j), j < 0, # int2bits(j) < i→n(i), 0 < i, i→n(i) < # int2bits(~ j), # int2bits(j) + 1 < # int2bits(~ j) ⊦ j + 2 ^ n→i(i→n(i) - 1) = 0, j = 0, band(j, 2 ^ i - 1) = bits2uint(fillsgn(i→n(i), int2bits(j))), i = 0

Rule argument

seq: ⊦ ¬(∃ i. j = ~(2 ^ i)) ∧ j < 0 → # int2bits(j) = # int2bits(~ j) subst: [j] → [j] rotate: F spec: int2bits inst: name: int2bits-len-neg-02

Additional information

Used simplifier rules: ⊦ ¬ n < n; Used terms: j