let K be non empty right_complementable add-associative right_zeroed doubleLoopStr ; :: thesis: for L being non empty right_complementable well-unital add-associative right_zeroed doubleLoopStr
for J being Function of K,L holds
( J is epimorphism iff opp J is antiepimorphism )
let L be non empty right_complementable well-unital add-associative right_zeroed doubleLoopStr ; :: thesis: for J being Function of K,L holds
( J is epimorphism iff opp J is antiepimorphism )
let J be Function of K,L; :: thesis: ( J is epimorphism iff opp J is antiepimorphism )
set J9 = opp J;
set L9 = opp L;
A1: ( rng J = the carrier of L iff rng (opp J) = the carrier of (opp L) ) ;
( J is linear iff opp J is antilinear ) by Th35;
hence ( J is epimorphism iff opp J is antiepimorphism ) by A1, Def10, Def11; :: thesis: verum