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Proof step 14 from proof and-false (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
bits = bits2 + boolvar0 ', bitsand(true ' + bits3, true ' + bits2) + (boolvar ∧ boolvar0)' = false ' + bits1, ∀ bits1, bits, bits0. # bits0 < #(bits3 + boolvar ') → bitsand(true ' + bits0, true ' + bits) = false ' + bits1 → false ⊦ bits = [], boolvar ∧ boolvar0 ∧ ¬ true ∈ bits1, ¬ false ∈ bitsand(true ' + bits3, true ' + bits2) ∧ boolvar ∧ boolvar0

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits, boolvar0, bits2] 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, bits2