A1: less_dom f,a c= X

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in less_dom f,a or x in X )
assume A2: x in less_dom f,a ; :: thesis: x in X
A3: x in dom f by A2, Def12;
A4: dom f c= X by RELAT_1:def 18;
thus x in X by A3, A4; :: thesis: verum

end;

thus less_dom f,a is Subset of X by A1; :: thesis: verum