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Proof step 180 from proof byte-law-and-one (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

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; Used terms: mklist(true, 8 - # bits1), bits2