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Proof step 17 from proof and-size-one (previous step)

bits1 = bits1.first ', 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 = [], bitsand(bits.butlast, bits0 + bits1.butlast) + (bits.last ∧ bits1.first)' = bits0 + bitsand(bits, bits1), bits0 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
bits = boolvar + bits3, bits1 = bits1.first ', boolvar, # 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 = [], bitsand(bits.butlast, bits0 + bits1.butlast) + (bits.last ∧ bits1.first)' = bits0 + bitsand(bits, bits1), bits0 = []

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits, boolvar, bits3] rotate: T spec: list-data inst: bitlista name: elim-list-c

Additional information

Used simplifier rules: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0; (elim) Used terms: bits, boolvar, bits3