let V be RealLinearSpace; :: thesis: for M1, M2 being Subset of V st M1 c= M2 holds
Circled-Family M2 c= Circled-Family M1
let M1, M2 be Subset of V; :: thesis: ( M1 c= M2 implies Circled-Family M2 c= Circled-Family M1 )
assume A1: M1 c= M2 ; :: thesis: Circled-Family M2 c= Circled-Family M1
let M be object ; :: according to TARSKI:def 3 :: thesis: ( not M in Circled-Family M2 or M in Circled-Family M1 )
assume A2: M in Circled-Family M2 ; :: thesis: M in Circled-Family M1
then reconsider M = M as Subset of V ;
M2 c= M by A2, Def2;
then A3: M1 c= M by A1;
M is circled by A2, Def2;
hence M in Circled-Family M1 by A3, Def2; :: thesis: verum