let X be non empty set ; :: thesis: for R being RMembership_Func of X,X holds 1 iter R = R
let R be RMembership_Func of X,X; :: thesis: 1 iter R = R
consider F being Function of NAT ,(Funcs [:X,X:],[.0 ,1.]) such that
A1: ( 1 iter R = F . 1 & F . 0 = Imf X,X & ( for k being natural number ex Q being RMembership_Func of X,X st
( F . k = Q & F . (k + 1) = Q (#) R ) ) ) by Def10;
consider Q being RMembership_Func of X,X such that
A2: ( F . 0 = Q & F . (0 + 1) = Q (#) R ) by A1;
thus 1 iter R = R by A1, A2, Th22; :: thesis: verum