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Proof step 31 from proof bitsor-bi-sgn (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
(¬ bits.first) ∈ bits.rest, bits ≠ [] ⊦ sgn(bits + boolvar0 ') = sgn(bits) + boolvar0 '
Proof step 33:
¬((¬ bits2.first) ∈ bits2.rest ∧ bits2 ≠ []), ∀ bits, bits1. # bits1 < #(bits3 + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits2int(bitsor(sgn(bits2 + boolvar '), bits3 + boolvar0 ')) = bits2int(bitsor(bits2, bits3) + (boolvar ∨ boolvar0)'), bits2 = [], bits3 = []
Proof step 68:
(¬ bits2.first) ∈ bits2.rest ∧ bits2 ≠ [], ∀ bits, bits1. # bits1 < #(bits3 + boolvar0 ') → true → bits ≠ [] ∧ bits1 ≠ [] → bits2int(bitsor(sgn(bits), bits1)) = bits2int(bitsor(bits, bits1)) ⊦ bits2int(bitsor(sgn(bits2) + boolvar ', bits3 + boolvar0 ')) = bits2int(bitsor(bits2, bits3) + (boolvar ∨ boolvar0)'), bits2 = [], bits3 = []

Rule argument

seq: (¬ bits.first) ∈ bits.rest, bits ≠ [] ⊦ sgn(bits + boolvar0 ') = sgn(bits) + boolvar0 ' subst: [boolvar0, bits] → [boolvar, bits2] rotate: F spec: bitopsaux inst: name: sgn-last-03

Additional information

Used terms: boolvar, bits2