let G be non empty multMagma ; :: thesis: for A, B, C being Subset of G holds A * (B /\ C) c= (A * B) /\ (A * C)
let A, B, C be Subset of G; :: thesis: A * (B /\ C) c= (A * B) /\ (A * C)
let x be set ; :: according to TARSKI:def 3 :: thesis: ( not x in A * (B /\ C) or x in (A * B) /\ (A * C) )
assume x in A * (B /\ C) ; :: thesis: x in (A * B) /\ (A * C)
then consider g1, g2 being Element of G such that
A1: ( x = g1 * g2 & g1 in A & g2 in B /\ C ) ;
( g2 in B & g2 in C ) by A1, XBOOLE_0:def 4;
then ( x in A * B & x in A * C ) by A1;
hence x in (A * B) /\ (A * C) by XBOOLE_0:def 4; :: thesis: verum