theorem Th39: :: CIRCCMB3:39

for x1, x2 being set
for X being non empty finite set
for f being Function of (2 -tuples_on X),X
for S being Signature of X st x2 in the carrier of S & not x1 in InnerVertices S & not Output (1GateCircStr (<*x1,x2*>,f)) in InputVertices S holds
InputVertices (S +* (1GateCircStr (<*x1,x2*>,f))) = (InputVertices S) \/ {x1}