Karnauch.md

2 variables (BA)

1. BA = 0
2. B = 0
3. B(1-A) = 1

3 variables (CBA)

1. C + B + A = 0
2. (1-B)(1-A) = 1
3. (1-C)(2 - B - A) = 1
4. C = 1
5. (2 - C + A)(2 - C + B) = 1
6. CB = 0
7. CBA = 0 (needs 2 constraints !!)

4 variables (DCBA)

1. D + C + B + A = 0
2. D + C + B = 0
3. D + C + BA = 1
4. D + C = 0
5. D + CB + CA = 0
6. D + CB = 0
7. D + CBA = 0
8. D = 0
9. D(C + B + A) = 0
10. D(C + B) = 0
11. DC + DBA = 0 (needs 2 constraints !!)
12. CD = 0
13. DC(B + A) = 0 (needs 2 constraints !!)
14. DCB = 0 (needs 2 constraints !!)
15. DCBA = 0 (needs 3 constraints !!)

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Lemmas

if p then a else b <=> (1-p)b + pa 

if p then 1 else b <=> (1-p)b + p
if p then 0 else b <=> (1-p)b
if p then a else 1 <=> 1 - p + pa 
if p then a else 0 <=> pa