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Proof step 260 from proof byte-law-and-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 261:
⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits)
Proof step 262:
¬ 8 ≤ # bitsand(bits, bits1), # bits = 8, int2bits(i) = bits0 + bits, # bits1 = 8, int2bits(j) = bits2 + bits1, 8 ≤ # bitsand(bits0, bits2) + # bitsand(bits, bits1) ⊦ bits0 = [], bits2 = [], bits = [], bits2 + bits1 = [], lastn(8, bitsand(bits0, bits2) + bitsand(bits, bits1)) = lastn(8, fillsgn(8, bitsand(bits2 + bits1, bits))), # bitsand(bits0, bits2) + # bitsand(bits, bits1) = 0
Proof step 268:
8 ≤ # bitsand(bits, bits1), # bits = 8, int2bits(i) = bits0 + bits, # bits1 = 8, int2bits(j) = bits2 + bits1, 8 ≤ # bitsand(bits0, bits2) + # bitsand(bits, bits1) ⊦ bits0 = [], bits2 = [], bits = [], bits2 + bits1 = [], lastn(8, bitsand(bits, bits1)) = lastn(8, fillsgn(8, bitsand(bits2 + bits1, bits))), # bitsand(bits0, bits2) + # bitsand(bits, bits1) = 0

Rule argument

seq: ⊦ n ≤ # bits → lastn(n, bits0 + bits) = lastn(n, bits) subst: [bits, bits0, n] → [bitsand(bits, bits1), bitsand(bits0, bits2), 8] rotate: F spec: list-del inst: bitlista name: lastN-append-01

Additional information

Used terms: bitsand(bits, bits1), bitsand(bits0, bits2), 8