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Proof step 25 from proof and-zerosin (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 26:
bits = bits3 + boolvar0 ', ∀ bits1, bits0. # bits1 < # bits → true ∈ bitsand(bits1, bits0) → bits1 = [] ∨ bits0 = [] ∨ true ∈ bits1 ⊦ bits = [], bits = bits.first ', bits2 + boolvar ' = (bits2 + boolvar ').first ', true ∈ bits, ¬ true ∈ bitsand(bits3, bits2) ∧ (¬ boolvar0 ∨ ¬ boolvar)

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits, boolvar0, bits3] 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, bits3