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Proof step 41 from proof and-ass (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
∀ bits2, bits0, bits1. # bits2 < # bits → true → bits2 = [] ∨ bits0 = [] ∨ bits1 = [] ∨ bitsand(bits2, bitsand(bits0, bits1)) = bitsand(bitsand(bits2, bits0), bits1) ⊦ bits0 = bits0.first ', bits3 + boolvar ' = (bits3 + boolvar ').first ', bits0 = [], bits = [], bitsand(bits, bitsand(bits0.butlast, bits3) + (bits0.last ∧ boolvar)') = bitsand(bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)', bits3 + boolvar '), bits = bits.first '

Rule argument

Additional information

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