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Proof step 26 from proof and-size-one (previous step)

bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits = true ', # bits0 + # bits1 = 0, bits1 = [], bits = [], bits1 = bits1.first ', bitsand(bits.butlast, bits0 + bits1.butlast) = bits0 + bitsand(bits.butlast, bits1.butlast), bits.butlast.first ∧ ¬ (# bits1 - 1) + 1 < # bits

User applied rule insert elim lemma

And obtained the following new goals

Proof step 27:
bits1 = bits3 + boolvar ', bits.first, # bits ≤ # bits1, ∀ bits2, bits1, bits0. # bits2 < # bits → # bits2 ≤ # bits1 ∧ bits2.first → bits2 = [] ∨ bitsand(bits2, bits0 + bits1) = bits0 + bitsand(bits2, bits1) ⊦ bits = true ', # bits0 + # bits1 = 0, bits1 = [], bits = [], bits1 = bits1.first ', bitsand(bits.butlast, bits0 + bits3) = bits0 + bitsand(bits.butlast, bits3), bits.butlast.first ∧ ¬ (# bits1 - 1) + 1 < # bits

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits1, 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: bits1, boolvar, bits3