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Proof step 14 from proof bitsand-app-false (previous step)

# bits2 < # bits0, ∀ bits, bits0, bits1. # bits1 < # bits2 → # bits1 < # bits0 → bitsand(bits + bits0, false ' + bits1) = bitsand(bits0, false ' + bits1) ∨ bits0 = [] ⊦ # bits + # bits0 = 0, bits2 = [], bits0 = [], bitsand(bits + bits0.butlast, false ' + bits2.butlast) + (bits0.last ∧ bits2.last)' = bitsand(bits0, false ' + bits2), # bits0 = 1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
bits2 = bits3 + boolvar ', # bits2 < # bits0, ∀ bits, bits0, bits1. # bits1 < # bits2 → # bits1 < # bits0 → bitsand(bits + bits0, false ' + bits1) = bitsand(bits0, false ' + bits1) ∨ bits0 = [] ⊦ # bits + # bits0 = 0, bits2 = [], bits0 = [], bitsand(bits + bits0.butlast, false ' + bits3) + (bits0.last ∧ boolvar)' = bitsand(bits0, false ' + bits2), # bits0 = 1

Rule argument

seq: bits ≠ [] ⊦ (boolvar ↔ bits.last) ∧ bits0 = bits.butlast ↔ bits = bits0 + boolvar ' subst: [bits, boolvar, bits0] → [bits2, 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: bits2, boolvar, bits3