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Proof step 11 from proof bitsand-len-false (previous step)

# bits1 ≤ # bits2, ∀ bits, bits0. # bits0 < # bits1 → # bits0 < # bits → # bitsand(bits, false ' + bits0) = 1 + # bits0 ∨ bits = [] ⊦ bits1 = [], # bitsand(bits2, false ' + bits1.butlast) = # bits1, bits2 = []

User applied rule insert elim lemma

And obtained the following new goals

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

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits1, boolvar, 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: bits1, boolvar, bits3