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Proof step 15 from proof add-ones-grlen-02 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 16:
bits0.butlast = boolvar + bits2 ∧ bits0.butlast ≠ [], # bits0 ≤ # bits, boolvar ∨ bitsand(bits.butlast, bits0.butlast) = bits0.butlast, ∀ bits, bits1. # bits1 < # bits0 → # bits1 ≤ # bits → bits1 = [] ∨ bitsand(bits, bits1) = bits1 ∨ false ∈ bits ∨ bits1.first ⊦ bits0 = [], bitsand(bits.butlast, bits0.butlast) + (bits.last ∧ bits0.last)' = bits0, # bits = 1, bits = [], # bits0 = 1, bits0 = false ', bits0.first, false ∈ bits, false ∈ bits.butlast

Rule argument

seq: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0) subst: [bits, boolvar, bits0] → [bits0.butlast, boolvar, bits2] rotate: T spec: list-data inst: bitlista name: elim-1

Additional information

Used simplifier rules: ⊦ bits ≠ [] → (bits.butlast = [] ↔ bits = bits.first ');%⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0); (elim) Used terms: bits0.butlast, boolvar, bits2