let H be non empty multMagma ; :: thesis: for P, Q being Subset of H
for h being Element of H st P c= Q holds
h * P c= h * Q
let P, Q be Subset of H; :: thesis: for h being Element of H st P c= Q holds
h * P c= h * Q
let h be Element of H; :: thesis: ( P c= Q implies h * P c= h * Q )
assume A1: P c= Q ; :: thesis: h * P c= h * Q
let x be object ; :: according to TARSKI:def 3 :: thesis: ( not x in h * P or x in h * Q )
assume x in h * P ; :: thesis: x in h * Q
then ex g being Element of H st
( x = h * g & g in P ) by GROUP_2:27;
hence x in h * Q by A1, GROUP_2:27; :: thesis: verum