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

bits2 = bits3 + boolvar ', # bits2 = n + # bits1, # bits1 ≤ # bits2, ∀ bits0, bits, n. # bits0 < # bits1 → # bits = n + 1 + # bits0 ∧ # bits0 < # bits → bits = [] ∨ bitsand(bits, true ' + bits0) = (true ' + mklist(true, n)) + bits0 ∨ false ∈ bits ⊦ bitsand(true ' + bits3, true ' + bits1.butlast) + (boolvar ∧ bits1.last)' = (true ' + mklist(true, n)) + bits1, bits1 = [], bits2 = [], false ∈ bits2

User applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
bits1 = bits4 + boolvar0 ', bits2 = bits3 + boolvar ', # bits2 = n + # bits1, # bits1 ≤ # bits2, ∀ bits0, bits, n. # bits0 < # bits1 → # bits = n + 1 + # bits0 ∧ # bits0 < # bits → bits = [] ∨ bitsand(bits, true ' + bits0) = (true ' + mklist(true, n)) + bits0 ∨ false ∈ bits ⊦ bitsand(true ' + bits3, true ' + bits4) + (boolvar ∧ boolvar0)' = (true ' + mklist(true, n)) + bits1, bits1 = [], bits2 = [], false ∈ bits2

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits1, boolvar0, bits4] 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, boolvar0, bits4