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Proof step 183 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(mklist(true, 8 - # bits1), bits2) + # bitsand(bits1, int2bits(i)), # bits1 < # bits0 + # bitsand(mklist(true, 8 - # bits1), bits2) + # bitsand(bits1, int2bits(i)), i < 0, # bits1 < 8, # bits1 < # bits0 + # bits2 + # bitsand(bits1, int2bits(i)), 8 ≤ # bits0 + # bits2 + # bitsand(bits1, int2bits(i)), 8 ≤ # bitsand(mklist(true, 8 - # bits1), bits2) + # bitsand(bits1, int2bits(i)), 8 ≤ # bits0 + # bitsand(mklist(true, 8 - # bits1), bits2) + # bitsand(bits1, int2bits(i)) ⊦ bits2 = [], lastn(8, (bits0 + bits2) + bitsand(bits1, int2bits(i))) = lastn(8, bitsand(mklist(true, 8 - # bits1), bits2) + bitsand(bits1, int2bits(i))), bitsand(mklist(true, 8 - # bits1), bits2) + bitsand(bits1, int2bits(i)) = [], bits1 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ ¬ false ∈ bits ∧ # bits ≤ # bits0 ∧ bits ≠ [] → bitsand(bits, bits0) = bits0 subst: [bits0, bits] → [bits2, mklist(true, 8 - # bits1)] rotate: F spec: intops inst: name: add-ones-lelen

Additional information

Used simplifier rules: ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ ¬ false ∈ mklist(true, n);% ⊦ # mklist(boolvar, n) = n;% ⊦ m < n → ¬ n < m;% ⊦ ¬ m ≤ n ↔ n < m;%n0 ≤ n ⊦ n - n0 ≤ m ↔ n ≤ m + n0;% ⊦ mklist(boolvar, m) = [] ↔ m = 0;% ⊦ n < m → m - n ≠ 0;% ⊦ m < n ∧ n ≤ n0 → m < n0; (forward)% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ n < n0 ∧ n0 < n1 → n +1 < n1; (forward) Used terms: bits2, mklist(true, 8 - # bits1)