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 antiisomorphism iff opp J is isomorphism )
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 antiisomorphism iff opp J is isomorphism )
let J be Function of K,L; :: thesis: ( J is antiisomorphism iff opp J is isomorphism )
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 antimonomorphism iff opp J is monomorphism ) by Th38;
hence ( J is antiisomorphism iff opp J is isomorphism ) by A1, Def12, Def13; :: thesis: verum