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Proof step 12 from proof and-false (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
bits2 = bits3 + boolvar ', bitsand(true ' + bits3, true ' + bits.butlast) + (boolvar ∧ bits.last)' = false ' + bits1, ∀ bits1, bits, bits0. # bits0 < # bits2 → bitsand(true ' + bits0, true ' + bits) = false ' + bits1 → false ⊦ bits = [], bits2 = [], ¬ false ∈ bitsand(true ' + bits3, true ' + bits.butlast) ∧ boolvar ∧ bits.last, boolvar ∧ bits.last ∧ ¬ true ∈ bits1

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits2, boolvar, 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: bits2, boolvar, bits3