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Proof step 30 from proof and-ass (previous step)

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, bits1.butlast) + (boolvar ∧ bits1.last)') = bitsand(bitsand(bits, bits3 + boolvar '), bits1), bits3 + boolvar ' = (bits3 + boolvar ').first ', bits1 = bits1.first '

User applied rule insert elim lemma

And obtained the following new goals

Proof step 31:
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 '

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits1, 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: bits1, boolvar0, bits4