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Proof step 237 from proof byte-law-and-one (previous step)

# bits = 8, int2bits(i) = bits0 + bits, # int2bits(j) ≤ 8, ~128 ≤ j, j < ~64, j < 0 ⊦ lastn(8, fillsgn(8, bits0 + bitsand(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 238:
⊦ n ≤ # bits → fillsgn(n, bits) = bits
Proof step 239:
¬ 8 ≤ # bitsand(bits, int2bits(j)), # bits = 8, int2bits(i) = bits0 + bits, # int2bits(j) ≤ 8, ~128 ≤ j, j < ~64, j < 0 ⊦ lastn(8, fillsgn(8, bits0 + bitsand(bits, int2bits(j)))) = lastn(8, fillsgn(8, bitsand(bits, int2bits(j)))), bitsand(bits, int2bits(j)) = [], bits0 = []
Proof step 242:
8 ≤ # bitsand(bits, int2bits(j)), # bits = 8, int2bits(i) = bits0 + bits, # int2bits(j) ≤ 8, ~128 ≤ j, j < ~64, j < 0 ⊦ lastn(8, fillsgn(8, bits0 + bitsand(bits, int2bits(j)))) = lastn(8, bitsand(bits, int2bits(j))), bitsand(bits, int2bits(j)) = [], bits0 = []

Rule argument

seq: ⊦ n ≤ # bits → fillsgn(n, bits) = bits subst: [bits, n] → [bitsand(bits, int2bits(j)), 8] rotate: F spec: bitopsaux inst: name: fillsgn-longer

Additional information

Used terms: bitsand(bits, int2bits(j)), 8