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Proof step 31 from proof and-sgn (previous step)

∀ bits1, bits. # bits1 < #(bits2 + boolvar ') → true → bits = [] ∨ bits1 = [] ∨ sgn(bitsand(sgn(bits), bits1)) = sgn(bitsand(bits, bits1)) ⊦ bits = [], sgn(bitsand(sgn(bits), bits2 + boolvar ')) = sgn(bitsand(bits.butlast, bits2) + (bits.last ∧ boolvar)'), bits = bits.first ', bits2 + boolvar ' = (bits2 + boolvar ').first '

User applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
bits = bits0 + boolvar0 ', ∀ bits1, bits. # bits1 < #(bits2 + boolvar ') → true → bits = [] ∨ bits1 = [] ∨ sgn(bitsand(sgn(bits), bits1)) = sgn(bitsand(bits, bits1)) ⊦ bits = [], sgn(bitsand(sgn(bits), bits2 + boolvar ')) = sgn(bitsand(bits0, bits2) + (boolvar0 ∧ boolvar)'), bits = bits.first ', bits2 + boolvar ' = (bits2 + boolvar ').first '

Rule argument

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