let G be _Graph; :: thesis: for X1, X2, Y1, Y2 being set st X1 c= X2 & Y1 c= Y2 holds
G .edgesBetween X1,Y1 c= G .edgesBetween X2,Y2
let X1, X2, Y1, Y2 be set ; :: thesis: ( X1 c= X2 & Y1 c= Y2 implies G .edgesBetween X1,Y1 c= G .edgesBetween X2,Y2 )
assume A1: ( X1 c= X2 & Y1 c= Y2 ) ; :: thesis: G .edgesBetween X1,Y1 c= G .edgesBetween X2,Y2

now

let e be set ; :: thesis: ( e in G .edgesBetween X1,Y1 implies e in G .edgesBetween X2,Y2 )
assume A2: e in G .edgesBetween X1,Y1 ; :: thesis: e in G .edgesBetween X2,Y2
then e SJoins X1,Y1,G by Def32;
then ( ( (the_Source_of G) . e in X1 & (the_Target_of G) . e in Y1 ) or ( (the_Source_of G) . e in Y1 & (the_Target_of G) . e in X1 ) ) by Def17;
then e SJoins X2,Y2,G by A1, A2, Def17;
hence e in G .edgesBetween X2,Y2 by Def32; :: thesis: verum

end;

hence G .edgesBetween X1,Y1 c= G .edgesBetween X2,Y2 by TARSKI:def 3; :: thesis: verum