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Proof step 19 from proof add-ones-grlen-02 (previous step)

bitsand(bits.butlast, false ' + bits3.butlast) = false ' + bits3.butlast, # bits3 < # bits, ∀ bits, bits1. # bits1 < #(false + bits3) → # bits1 ≤ # bits → bits1 = [] ∨ bitsand(bits, bits1) = bits1 ∨ false ∈ bits ∨ bits1.first ⊦ bits3.butlast + (bits.last ∧ bits3.last)' = bits3, bits3 = [], bits = [], # bits = 1, false ∈ bits.butlast, false ∈ bits

User applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
bits3 = bits0 + boolvar ', bitsand(bits.butlast, false ' + bits0) = false ' + bits0, # bits3 < # bits, ∀ bits, bits1. # bits1 < #(false + bits3) → # bits1 ≤ # bits → bits1 = [] ∨ bitsand(bits, bits1) = bits1 ∨ false ∈ bits ∨ bits1.first ⊦ bits0 + (bits.last ∧ boolvar)' = bits3, bits3 = [], bits = [], # bits = 1, false ∈ bits.butlast, false ∈ bits

Rule argument

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