reserve A,B,C,Y,x,y,z for set, U, D for non empty set,
X for non empty Subset of D, d,d1,d2 for Element of D;
reserve P,Q,R for Relation, g for Function, p,q for FinSequence;
reserve f for BinOp of D, i,m,n for Nat;
reserve X for set, f for Function;
reserve U1,U2 for non empty set;

theorem (chi(A,B))"{0}=B\A & (chi(A,B))"{1}=A/\B ::#Th24
proof
set f=B\A --> 0, g=A/\B --> 1, IT=chi(A,B);
A1: 0 in {0} & 1 in {1} & not 1 in {0} & not 0 in {1} by TARSKI:def 1;
A2: f"{1}={} & g"{0}={} by A1, FUNCOP_1:16;
thus IT"{0} =(f\/g)"{0} by Lm40.=f"{0}\/g"{0} by Th23.= B\A
by A1, FUNCOP_1:14, A2;
thus IT"{1} =(f\/g)"{1} by Lm40.=f"{1}\/g"{1} by Th23.= A/\B
by A1,FUNCOP_1:14, A2;
end;
