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Proof step 9 from proof bitsand-len-true (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

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

Rule argument

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