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Proof step 19 from proof sgn-ex-01 (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 20:
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

Rule argument

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

Additional information

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