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Proof step 859 from proof bitsand-cast (previous step)

# bitsand(boolvar ' + boolvar0 ' + bits, bits0) ≤ 2 + # bits + m ∧ bitsand(boolvar ' + boolvar0 ' + bits, bits0) ≠ [], sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, bits0.first, # bits0 ≤ 2 + # bits, # bits0 ≤ (2 + # bits) + # bits2, 2 + # bits ≤ # bitsand(boolvar ' + boolvar0 ' + bits, bits0), # bits0 ≤ # bitsand(boolvar ' + boolvar0 ' + bits, bits0) ⊦ boolvar ↔ boolvar0, lastn (2 + # bits + m, mklist(bitsand(boolvar ' + boolvar0 ' + bits, bits0).first, 2 + # bits + m - # bitsand(boolvar ' + boolvar0 ' + bits, bits0)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)) = lastn(2 + # bits + m, mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), bits0 = [], boolvar ∧ boolvar0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 860:
sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, # bits0 ≤ 2 + # bits + m, # bits0 ≤ # bitsand(boolvar ' + boolvar0 ' + bits, bits0), 2 + # bits ≤ # bitsand(boolvar ' + boolvar0 ' + bits, bits0), # bits0 ≤ (2 + # bits) + # bits2, # bits0 ≤ 2 + # bits, bits0.first, # bitsand(boolvar ' + boolvar0 ' + bits, bits0) ≤ 2 + # bits + m ⊦ bits0 = [], lastn (2 + # bits + m, mklist(bitsand(boolvar ' + boolvar0 ' + bits, bits0).first, 2 + # bits + m - # bitsand(boolvar ' + boolvar0 ' + bits, bits0)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)) = lastn(2 + # bits + m, mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), boolvar ↔ boolvar0, boolvar ∧ boolvar0

Rule argument

Additional information

Used simplifier rules: and-notempty-02: ⊦ bits0 ≠ [] → bitsand(boolvar ' + bits, bits0) ≠ [];% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m ≤ m + n;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward)% ⊦ m + n = n + m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;