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Proof step 131 from proof byte-law-and-one (previous step)

8 = # fillsgn(8, bitsand(bits, fillsgn(8, int2bits(i)))), 8 = # fillsgn(8, bitsand(bits, int2bits(i))), 7 = # fillsgn(7, int2bits(i)), int2bits(j) = bits0 + bits, # bits = 8, 0 ≤ i, # int2bits(i) < 8 ⊦ fillsgn(8, bitsand(bits, int2bits(i))) = fillsgn(8, bitsand(bits, fillsgn(8, int2bits(i)))), bits0 + bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] ∧ bits0 ≠ [] → bitsand(bits, bits0) = bitsand(bits0, bits) subst: [bits0, bits] → [fillsgn(8, int2bits(i)), bits] rotate: F spec: intops inst: name: and-com

Additional information

Used simplifier rules: ⊦ fillsgn(n, bits) = [] ↔ bits = [] ∧ n = 0;% ⊦ int2bits(j) ≠ [];% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ # [] = 0; Used terms: fillsgn(8, int2bits(i)), bits