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Proof step 20 from proof sgn-ex-01 (previous step)

sgn(mklist(false, n) + true ' + bits) = false ' + true ' + bits ⊦ n = 0, true ' + mklist(false, n) + true ' + bits = mklist(true, 1) + false ' + mklist(false, n -1) + true ' + bits ∧ sgn(mklist(true, 1) + false ' + mklist(false, n -1) + true ' + bits) = true ' + false ' + mklist(false, n -1) + true ' + bits ∧ ¬(true ↔ false) ∧ 1 ≠ 0, ∃ boolvar2, n0, boolvar3, bits1. true ' + mklist(false, n) + true ' + 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 21:
sgn(mklist(false, n) + true ' + bits) = false ' + true ' + bits ⊦ n = 0, mklist(false, n) = false ' + mklist(false, n - 1), ∃ boolvar2, n0, boolvar3, bits1. true ' + mklist(false, n) + true ' + 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-01: ⊦ sgn(true ' + false ' + bits) = true ' + false ' + 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(true, (* n)) = true ' + mklist(true, n -1);% ⊦ (bits + bits0) + bits1 = bits + bits0 + bits1;