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Proof step 839 from proof bitsand-cast (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 840:
sgn(mklist(boolvar, m) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits, # bits2 + # bitsand(boolvar ' + boolvar0 ' + bits, bits0) < 2 + # bits, # bits0 ≤ 2 + # bits, bits0.first ⊦ lastn(2 + # bits + m, fillsgn(2 + # bits + m, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(2 + # bits + m, fillsgn(2 + # bits + m, (bits2 + mklist(boolvar, m)) + bitsand(boolvar ' + boolvar0 ' + bits, bits0))), boolvar ↔ boolvar0, bits0 = [], boolvar ∧ boolvar0

Rule argument

Additional information

Used simplifier rules: n < n0 ⊦ (* n) ≠ m0 + (* n0);% ⊦ m < n → n ≠ 0; (forward)% ⊦ m + n = n + m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m + n ≤ m + n0 ↔ n ≤ n0;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # mklist(boolvar, n) = n;% ⊦ #(bits + bits0) = # bits + # bits0;