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Proof step 21 from proof uint2bits-add-high-02 (previous step)

0 ≤ j0 + 2 ^ i, 2 ^ (i - 1) + j0 < 0, 0 < i, j0 < 0 ⊦ sgn(int2bits(j0).rest) = sgn(fillsgn(i→n(i), int2bits(j0).rest)), fillsgn(i→n(i), int2bits(j0).rest) = [], fillsgn(i→n(i), int2bits(j0).rest).first

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ bits ≠ [] → sgn(fillsgn(n, bits)) = sgn(bits)
Proof step 23:
¬ int2bits(j0).rest ≠ [], 0 ≤ j0 + 2 ^ i, 2 ^ (i - 1) + j0 < 0, 0 < i, j0 < 0 ⊦ sgn(int2bits(j0).rest) = sgn(fillsgn(i→n(i), int2bits(j0).rest)), fillsgn(i→n(i), int2bits(j0).rest) = [], fillsgn(i→n(i), int2bits(j0).rest).first

Rule argument

seq: ⊦ bits ≠ [] → sgn(fillsgn(n, bits)) = sgn(bits) subst: [bits, n] → [int2bits(j0).rest, i→n(i)] rotate: F spec: bitopsaux inst: name: sgn-fill

Additional information

Used terms: int2bits(j0).rest, i→n(i)