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Proof step 382 from proof bitsand-cast (previous step)

¬(# bits0 ≤ #(boolvar ' + boolvar0 ' + bits) ∧ bits0 ≠ [] ∧ bits0.first), ¬(# bits0 ≤ #(boolvar ' + boolvar0 ' + bits) ∧ bits0 ≠ [] ∧ ¬ bits0.first), sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ boolvar ↔ boolvar0, bits0 = [], n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits, bits0))), boolvar ∧ boolvar0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 383:
sgn(mklist(boolvar, n - 1) + boolvar ' + boolvar0 ' + bits) = boolvar ' + boolvar0 ' + bits ⊦ boolvar ↔ boolvar0, bits0 = [], n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(boolvar ' + boolvar0 ' + bits, bits0))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand((bits2 + mklist(boolvar, n - 1)) + boolvar ' + boolvar0 ' + bits, bits0))), boolvar ∧ boolvar0, ¬ 2 + # bits < # bits0 ∧ ¬ bits0.first, ¬ 2 + # bits < # bits0 ∧ bits0.first

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ m ≤ n ↔ n < m;% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ # boolvar ' = 0 +1;% ⊦ #(bits + bits0) = # bits + # bits0;