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Proof step 45 from proof and-ass (previous step)

bits0 = bits + boolvar1 ', ∀ bits2, bits0, bits1. # bits2 < #(bits4 + boolvar0 ') → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits0 = bits0.first ', bits3 + boolvar ' = (bits3 + boolvar ').first ', bits0 = [], bitsand(bits4 + boolvar0 ', bitsand(bits, bits3) + (boolvar1 ∧ boolvar)') = bitsand(bitsand(bits4, bits) + (boolvar0 ∧ boolvar1)', bits3 + boolvar '), bits4 + boolvar0 ' = (bits4 + boolvar0 ').first '

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
∀ bits2, bits0, bits1. # bits2 < #(bits4 + boolvar0 ') → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits + boolvar1 ' = (bits + boolvar1 ').first ', bits3 + boolvar ' = (bits3 + boolvar ').first ', bitsand(bits4 + boolvar0 ', bitsand(bits, bits3) + (boolvar1 ∧ boolvar)') = bitsand(bitsand(bits4, bits) + (boolvar0 ∧ boolvar1)', bits3 + boolvar '), bits4 + boolvar0 ' = (bits4 + boolvar0 ').first '

Rule argument

Additional information

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