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Proof step 16 from proof sgn-ex-01 (previous step)

sgn(mklist(true, n) + false ' + bits) = true ' + false ' + bits ⊦ n = 0, false ' + mklist(true, n) + false ' + bits = mklist(false, 1) + true ' + mklist(true, n -1) + false ' + bits ∧ sgn(mklist(false, 1) + true ' + mklist(true, n -1) + false ' + bits) = false ' + true ' + mklist(true, n -1) + false ' + bits ∧ ¬(false ↔ true) ∧ 1 ≠ 0, ∃ boolvar2, n0, boolvar3, bits1. false ' + mklist(true, n) + false ' + bits = mklist(boolvar2, n0) + boolvar3 ' + bits1 ∧ sgn(mklist(boolvar2, n0) + boolvar3 ' + bits1) = boolvar2 ' + boolvar3 ' + bits1 ∧ ¬(boolvar2 ↔ boolvar3) ∧ n0 ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
sgn(mklist(true, n) + false ' + bits) = true ' + false ' + bits ⊦ n = 0, mklist(true, n) = true ' + mklist(true, n - 1), ∃ boolvar2, n0, boolvar3, bits1. false ' + mklist(true, n) + false ' + bits = mklist(boolvar2, n0) + boolvar3 ' + bits1 ∧ sgn(mklist(boolvar2, n0) + boolvar3 ' + bits1) = boolvar2 ' + boolvar3 ' + bits1 ∧ ¬(boolvar2 ↔ boolvar3) ∧ n0 ≠ 0

Rule argument

Additional information

Used simplifier rules: sgn-base-02: ⊦ sgn(false ' + true ' + bits) = false ' + true ' + bits;% ⊦ bits + bits0 = bits1 + bits0 ↔ bits = bits1;% ⊦ bits + bits0 = bits + bits1 ↔ bits0 = bits1;% ⊦ n -1 = n - 1;% ⊦ bits + [] = bits;% ⊦ mklist(boolvar, 0) = [];%n ≠ 0 ⊦ mklist(false, (* n)) = false ' + mklist(false, n -1);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;