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Proof step 12 from proof add-ones-lelen (previous step)

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

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

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

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0 subst: [bits, boolvar, bits0] → [bits0, 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: bits0, boolvar, bits3