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Proof step 15 from proof sgn-ex-01 (previous step)

sgn(mklist(true, n) + false ' + bits) = true ' + false ' + bits ⊦ n = 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

User applied rule exists right

And obtained the following new goals

Proof step 16:
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

Rule argument

pos: right 2 terms: false, 1, true, mklist(true, n -1) + false ' + bits abort: F discard: F computed: F

Additional information

Used terms: false, 1, true, mklist(true, n -1) + false ' + bits