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Proof step 272 from proof byte-law-and-one (previous step)

# bits = 8, int2bits(i) = bits0 + bits, # bits1 = 8, int2bits(j) = bits2 + bits1, 8 ≤ # bitsand(bits1, bits), 8 ≤ # bitsand(bits0, bits2) + # bitsand(bits1, bits) ⊦ bits = [], bits1 = [], bits0 = [], bits2 = [], bits2 + bits1 = [], lastn(8, bitsand(bits1, bits)) = lastn(8, fillsgn(8, bitsand(bits2 + bits1, bits))), # bitsand(bits0, bits2) + # bitsand(bits1, bits) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 273:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1)
Proof step 274:
¬(# bits ≤ # bits1 ∧ bits ≠ [] ∧ bits.first), # bits = 8, int2bits(i) = bits0 + bits, # bits1 = 8, int2bits(j) = bits2 + bits1, 8 ≤ # bitsand(bits1, bits), 8 ≤ # bitsand(bits0, bits2) + # bitsand(bits1, bits) ⊦ bits = [], bits1 = [], bits0 = [], bits2 = [], bits2 + bits1 = [], lastn(8, bitsand(bits1, bits)) = lastn(8, fillsgn(8, bitsand(bits2 + bits1, bits))), # bitsand(bits0, bits2) + # bitsand(bits1, bits) = 0
Proof step 277:
# bits ≤ # bits1 ∧ bits ≠ [] ∧ bits.first, # bits = 8, int2bits(i) = bits0 + bits, # bits1 = 8, int2bits(j) = bits2 + bits1, 8 ≤ # bitsand(bits1, bits), 8 ≤ # bitsand(bits0, bits2) + # bitsand(bits1, bits) ⊦ bits = [], bits1 = [], bits0 = [], bits2 = [], bits2 + bits1 = [], lastn(8, bitsand(bits1, bits)) = lastn(8, fillsgn(8, bits2 + bitsand(bits1, bits))), # bitsand(bits0, bits2) + # bitsand(bits1, bits) = 0

Rule argument

seq: ⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1) subst: [bits1, bits0, bits] → [bits, bits1, bits2] rotate: F spec: intops inst: name: bitsand-app-true

Additional information

Used terms: bits, bits1, bits2