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Proof step 7 from proof bitsor-sgn-in (previous step)

sgn(mklist(boolvar0, n) + boolvar1 ' + bits1) = boolvar0 ' + boolvar1 ' + bits1 ⊦ bits0 = [], boolvar ∈ bitsor(boolvar0 ' + boolvar1 ' + bits1, bits0) ↔ boolvar ∈ bitsor(mklist(boolvar0, n) + boolvar1 ' + bits1, bits0), n = 0, boolvar0 ↔ boolvar1, ¬ true ∈ mklist(boolvar0, n) ∧ ¬ boolvar1 ∧ ¬ true ∈ bits1, ¬ false ∈ mklist(boolvar0, n) ∧ boolvar1 ∧ ¬ false ∈ bits1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ≠ 0 ∧ bits0 ≠ [] → (boolvar ∈ bitsor(mklist(boolvar0, n) + bits, bits0) ↔ boolvar ∈ bitsor(boolvar0 ' + bits, bits0))

Rule argument

name: bitsor-mklist-in rotate: F subst: [bits0, bits, n, boolvar0, boolvar] → [bits0, boolvar1 ' + bits1, n, boolvar0, boolvar]

Additional information

Used simplifier rules: ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1; Used terms: bits0, boolvar1 ' + bits1, n, boolvar0, boolvar