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Proof step 228 from proof byte-law-and-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 229:
⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1)
Proof step 230:
¬(# int2bits(j) ≤ # bits ∧ int2bits(j) ≠ [] ∧ int2bits(j).first), # bits = 8, int2bits(i) = bits0 + bits, # int2bits(j) = 8 ⊦ lastn(8, fillsgn(8, bitsand(bits0 + bits, int2bits(j)))) = lastn(8, fillsgn(8, bitsand(bits, int2bits(j)))), bitsand(bits, int2bits(j)) = [], bits0 = []
Proof step 236:
# int2bits(j) ≤ # bits ∧ int2bits(j) ≠ [] ∧ int2bits(j).first, # bits = 8, int2bits(i) = bits0 + bits, # int2bits(j) = 8 ⊦ lastn(8, fillsgn(8, bits0 + bitsand(bits, int2bits(j)))) = lastn(8, fillsgn(8, bitsand(bits, int2bits(j)))), bitsand(bits, int2bits(j)) = [], bits0 = []

Rule argument

seq: ⊦ # bits1 ≤ # bits0 ∧ bits1 ≠ [] ∧ bits1.first → bitsand(bits + bits0, bits1) = bits + bitsand(bits0, bits1) subst: [bits1, bits0, bits] → [int2bits(j), bits, bits0] rotate: F spec: intops inst: name: bitsand-app-true

Additional information

Used terms: int2bits(j), bits, bits0