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Proof step 862 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 863:
sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, # bits0 ≤ (2 + # bits) + # bits2, bits0.first, # bits0 ≤ 2 + # bits + m, # bits0 ≤ 2 + # bits ⊦ boolvar ↔ boolvar0, bits0 = [], lastn(2 + # bits + m, mklist(bitsand(boolvar ' + boolvar0 ' + bits, bits0).first, m) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)) = lastn(2 + # bits + m, mklist(boolvar, m) + bitsand(boolvar ' + boolvar0 ' + bits, bits0)), boolvar ∧ boolvar0

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m + n;% ⊦ m ≤ m;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ 0 + m = m;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ m + n - n + n1 = m - n1;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;