
theorem Th28:
for F be Function, x,y be object st x in dom F & y in dom F holds
 F,Swap(F,x,y) are_fiberwise_equipotent
proof
    let F be Function, x,y be object;
    assume A1: x in dom F & y in dom F;
A2: dom(Swap(F,x,y)) = dom F by FUNCT_7:99;
A3: dom(Swap(id dom F,x,y)) = dom(id dom F) by FUNCT_7:99;
A4: rng(Swap(id dom F,x,y)) = rng(id dom F) by FUNCT_7:103;
    Swap(F,x,y) = F*Swap(id dom F,x,y) by A1,Th27;
    hence thesis by A1,A2,A3,A4,CLASSES1:77;
end;
