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Proof step 186 from proof byte-law-and-one (previous step)

7 = # fillsgn(7, int2bits(i)), # bits1 = # int2bits(i), int2bits(j) = (bits0 + bits2) + bits1, # bits2 + # bits1 = 8, 8 ≤ # bits0 + # bits2 + # bitsand(bits1, int2bits(i)), 8 ≤ # bits2 + # bitsand(bits1, int2bits(i)), # bits1 < # bits2 + # bitsand(bits1, int2bits(i)), # bits1 < # bits0 + # bits2 + # bitsand(bits1, int2bits(i)), # bits1 < 8, i < 0 ⊦ bits1 = [], bits2 + bitsand(bits1, int2bits(i)) = [], lastn(8, (bits0 + bits2) + bitsand(bits1, int2bits(i))) = lastn(8, bits2 + bitsand(bits1, int2bits(i))), bits2 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 187:
⊦ (bits + bits0) + bits1 = bits + bits0 + bits1
Proof step 188:
7 = # fillsgn(7, int2bits(i)), # bits1 = # int2bits(i), int2bits(j) = (bits0 + bits2) + bits1, # bits2 + # bits1 = 8, 8 ≤ # bits0 + # bits2 + # bitsand(bits1, int2bits(i)), 8 ≤ # bits2 + # bitsand(bits1, int2bits(i)), # bits1 < # bits2 + # bitsand(bits1, int2bits(i)), # bits1 < # bits0 + # bits2 + # bitsand(bits1, int2bits(i)), # bits1 < 8, i < 0 ⊦ bits1 = [], bits2 + bitsand(bits1, int2bits(i)) = [], lastn(8, bits0 + bits2 + bitsand(bits1, int2bits(i))) = lastn(8, bits2 + bitsand(bits1, int2bits(i))), bits2 = []

Rule argument

seq: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1 subst: [bits1, bits0, bits] → [bitsand(bits1, int2bits(i)), bits2, bits0] rotate: F spec: list inst: bitlista name: a

Additional information

Used terms: bitsand(bits1, int2bits(i)), bits2, bits0