let G be non empty multMagma ; :: thesis: for g1, g2, g being Element of G holds {g1,g2} * {g} = {(g1 * g),(g2 * g)}
let g1, g2, g be Element of G; :: thesis: {g1,g2} * {g} = {(g1 * g),(g2 * g)}
thus {g1,g2} * {g} c= {(g1 * g),(g2 * g)} :: according to XBOOLE_0:def 10 :: thesis: {(g1 * g),(g2 * g)} c= {g1,g2} * {g}

proof

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in {g1,g2} * {g} or x in {(g1 * g),(g2 * g)} )
assume x in {g1,g2} * {g} ; :: thesis: x in {(g1 * g),(g2 * g)}
then consider h1, h2 being Element of G such that
A1: x = h1 * h2 and
A2: ( h1 in {g1,g2} & h2 in {g} ) ;
( h2 = g & ( h1 = g1 or h1 = g2 ) ) by A2, TARSKI:def 1, TARSKI:def 2;
hence x in {(g1 * g),(g2 * g)} by A1, TARSKI:def 2; :: thesis: verum

end;

let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in {(g1 * g),(g2 * g)} or x in {g1,g2} * {g} )
assume x in {(g1 * g),(g2 * g)} ; :: thesis: x in {g1,g2} * {g}
then ( ( x = g1 * g or x = g2 * g ) & g in {g} & g1 in {g1,g2} & g2 in {g1,g2} ) by TARSKI:def 1, TARSKI:def 2;
hence x in {g1,g2} * {g} ; :: thesis: verum