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Proof step 42 from proof and-ass (previous step)

∀ 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 '

User applied rule insert elim lemma

And obtained the following new goals

Proof step 43:
bits = bits4 + boolvar0 ', ∀ 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(bits4, bits0.butlast) + (boolvar0 ∧ bits0.last)', bits3 + boolvar '), bits = bits.first '

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits, boolvar0, bits4] rotate: T spec: list-last inst: bitlista name: last-elim

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar '; (elim) Used terms: bits, boolvar0, bits4