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Proof step 177 from proof byte-law-and-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ # bits = # bits1 ∧ bits0 ≠ [] ∧ bits2 ≠ [] ∧ bits ≠ [] → bitsand(bits0 + bits, bits2 + bits1) = bitsand(bits0, bits2) + bitsand(bits, bits1) subst: [bits1, bits2, bits, bits0] → [int2bits(i), mklist(true, 8 - # bits1), bits1, bits2] rotate: F spec: intops inst: name: bitsand-app

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ n < m → m - n ≠ 0;% ⊦ # [] = 0;% ⊦ # bits = 0 ↔ bits = [];% ⊦ int2bits(j) ≠ []; Used terms: int2bits(i), mklist(true, 8 - # bits1), bits1, bits2