- 4.
- Prove x
L' iff f(x)
L, where L' is CIRCUIT-SAT, L is
SAT, and f is the construction above.
x CIRCUIT-SAT f(x) SAT
If C has a satisfying assignment, then each wire is well-defined and the output is 1.

Therefore, each conjunct of is 1, and will evaluate to 1.

A satisfying assignment to yields a valid circuit C whose output is 1.