let G be _Graph; :: thesis: for X being set
for E being Subset of (the_Edges_of G)
for H being reverseEdgeDirections of G,X st E is RepEdgeSelection of G holds
E is RepEdgeSelection of H
let X be set ; :: thesis: for E being Subset of (the_Edges_of G)
for H being reverseEdgeDirections of G,X st E is RepEdgeSelection of G holds
E is RepEdgeSelection of H
let E be Subset of (the_Edges_of G); :: thesis: for H being reverseEdgeDirections of G,X st E is RepEdgeSelection of G holds
E is RepEdgeSelection of H
let H be reverseEdgeDirections of G,X; :: thesis: ( E is RepEdgeSelection of G implies E is RepEdgeSelection of H )
assume A1: E is RepEdgeSelection of G ; :: thesis: E is RepEdgeSelection of H
A2: E is Subset of (the_Edges_of H) by GLIB_007:4;

now :: thesis: for v, w, e0 being object st e0 Joins v,w,H holds
ex e being object st
( e Joins v,w,H & e in E & ( for e9 being object st e9 Joins v,w,H & e9 in E holds
e9 = e ) )

let v, w, e0 be object ; :: thesis: ( e0 Joins v,w,H implies ex e being object st
( e Joins v,w,H & e in E & ( for e9 being object st e9 Joins v,w,H & e9 in E holds
e9 = e ) ) )
assume e0 Joins v,w,H ; :: thesis: ex e being object st
( e Joins v,w,H & e in E & ( for e9 being object st e9 Joins v,w,H & e9 in E holds
e9 = e ) )
then consider e being object such that
A3: ( e Joins v,w,G & e in E ) and
A4: for e9 being object st e9 Joins v,w,G & e9 in E holds
e9 = e by A1, GLIB_007:9, GLIB_009:def 5;
take e = e; :: thesis: ( e Joins v,w,H & e in E & ( for e9 being object st e9 Joins v,w,H & e9 in E holds
e9 = e ) )
thus ( e Joins v,w,H & e in E ) by A3, GLIB_007:9; :: thesis: for e9 being object st e9 Joins v,w,H & e9 in E holds
e9 = e
let e9 be object ; :: thesis: ( e9 Joins v,w,H & e9 in E implies e9 = e )
assume ( e9 Joins v,w,H & e9 in E ) ; :: thesis: e9 = e
hence e9 = e by A4, GLIB_007:9; :: thesis: verum

end;

hence E is RepEdgeSelection of H by A2, GLIB_009:def 5; :: thesis: verum