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Proof step 31 from proof and-ass (previous step)

bits1 = bits4 + boolvar0 ', bits = bits.first ', ∀ bits2, bits0, bits1. # bits2 < # bits → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits1 = [], bits = [], bitsand(bits, bitsand(bits3, bits4) + (boolvar ∧ boolvar0)') = bitsand(bitsand(bits, bits3 + boolvar '), bits1), bits3 + boolvar ' = (bits3 + boolvar ').first ', bits1 = bits1.first '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
bits = bits.first ', ∀ bits2, bits0, bits1. # bits2 < # bits → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits = [], bitsand(bits, bitsand(bits3, bits4) + (boolvar ∧ boolvar0)') = bitsand(bitsand(bits, bits3 + boolvar '), bits4 + boolvar0 '), bits3 + boolvar ' = (bits3 + boolvar ').first ', bits4 + boolvar0 ' = (bits4 + boolvar0 ').first '

Rule argument

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;% ⊦ bits + boolvar ' ≠ [];