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Proof step 21 from proof cast-law-and-one (previous step)

bitsand(sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0)) ≠ [], 0 < i ⊦ bits2int(lastn(i→n(i), fillsgn(i→n(i), bitsand(int2bits(j), int2bits(j0))))) = bits2int(lastn(i→n(i), fillsgn(i→n(i), sgn(bitsand(sgn(lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))), int2bits(j0))))))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

name: and-sgn rotate: F subst: [bits0, bits] → [int2bits(j0), lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))]

Additional information

Used simplifier rules: ⊦ bits ≠ [] → lastn(n, fillsgn(n, sgn(bits))) = lastn(n, fillsgn(n, bits));% ⊦ lastn(n, bits) = [] ↔ n = 0;% ⊦ i→n(i) = 0 ↔ i = 0;% ⊦ int2bits(j) ≠ [];% ⊦ fillsgn(0, bits) = bits;% ⊦ lastn(0, bits) = [];% ⊦ sgn([]) = []; Used terms: int2bits(j0), lastn(i→n(i), fillsgn(i→n(i), int2bits(j)))