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Proof step 11 from proof bitsand-zeros-01 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
bits = bits3 + boolvar0 ', 2 + # bits2 < # bits, ∀ bits1, bits0. # bits0 < # bits → 1 + # bits1 < # bits0 → bits0 = [] ∨ bitsand(bits0, false ' + bits1) = false ' + mklist(false, # bits1) ∨ true ∈ bits0 ⊦ # bits = 1, bits = [], bitsand(bits3, false ' + bits2) + (boolvar0 ∧ boolvar)' = false ' + false ' + mklist(false, # bits2), true ∈ bits

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits, boolvar0, bits3] 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: bits, boolvar0, bits3