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Proof step 69 from proof bitsor-bi-sgn (previous step)

(¬ bits2.first) ∈ bits2.rest, ∀ bits, bits1. # bits1 < #(bits3 + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits2 = [], bits3 = [], bits2int(bitsor(sgn(bits2) + boolvar ', bits3 + boolvar0 ')) = bits2int(bitsor(bits2, bits3) + (boolvar ∨ boolvar0)')

User applied rule insert elim lemma

And obtained the following new goals

Rule argument

seq: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0) subst: [bits, boolvar, bits0] → [bits2, boolvar1, bits0] rotate: T spec: list-data inst: bitlista name: elim-1

Additional information

Used simplifier rules: ⊦ bits ≠ [] → ( (boolvar ↔ bits.first) ∧ bits0 = bits.rest ↔ bits = boolvar + bits0); (elim) Used terms: bits2, boolvar1, bits0