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Proof step 124 from proof byte-law-and-one (previous step)

8 = # fillsgn(8, bitsand(bits, int2bits(i))), 7 = # fillsgn(7, int2bits(i)), int2bits(j) = bits0 + bits, # bits = 8, # int2bits(i) < # bitsand(bits, false ' + fillsgn(7, int2bits(i))), 0 ≤ i, # int2bits(i) < 8, 8 < # bitsand(bits, false ' + fillsgn(7, int2bits(i))), # int2bits(i) + 1 < # bitsand(bits, false ' + fillsgn(7, int2bits(i))) ⊦ fillsgn(8, bitsand(bits, int2bits(i))) = lastn(8, bitsand(bits, false ' + fillsgn(7, int2bits(i)))), bits0 + bits = [], 8 = # fillsgn(8, bitsand(bits, false ' + fillsgn(7, int2bits(i)))), bitsand(bits, false ' + fillsgn(7, int2bits(i))) = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits0.first ∧ # bits0 ≤ # bits ∧ bits0 ≠ [] → # bitsand(bits, bits0) = # bits subst: [bits0, bits] → [false ' + fillsgn(7, int2bits(i)), bits] rotate: F spec: intops inst: name: bitsand-len-true

Additional information

Used simplifier rules: ⊦ boolvar ' + bits ≠ [];% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ (boolvar ' + bits).first ↔ boolvar; Used terms: false ' + fillsgn(7, int2bits(i)), bits