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Proof step 9 from proof bitsand-app (previous step)

# bits = # bits4 + 1, ∀ bits2, bits0, bits, bits3. # bits3 < #(bits4 + boolvar ') → # bits = # bits3 → bits0 = [] ∨ bits2 = [] ∨ bits = [] ∨ bitsand(bits0 + bits, bits2 + bits3) = bitsand(bits0, bits2) + bitsand(bits, bits3) ⊦ bits = [], bits2 = [], bits0 = [], bitsand(bits0 + bits.butlast, bits2 + bits4) + (bits.last ∧ boolvar)' = bitsand(bits0, bits2) + bitsand(bits, bits4 + boolvar ')

User applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
bits = bits1 + boolvar0 ', # bits = # bits4 + 1, ∀ bits2, bits0, bits, bits3. # bits3 < #(bits4 + boolvar ') → # bits = # bits3 → bits0 = [] ∨ bits2 = [] ∨ bits = [] ∨ bitsand(bits0 + bits, bits2 + bits3) = bitsand(bits0, bits2) + bitsand(bits, bits3) ⊦ bits = [], bits2 = [], bits0 = [], bitsand(bits0 + bits1, bits2 + bits4) + (boolvar0 ∧ boolvar)' = bitsand(bits0, bits2) + bitsand(bits, bits4 + boolvar ')

Rule argument

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