consider f being Element of FuncsT X, T1, T2 being Element of TOL X such that
W:
( m = [[T1,T2],f] & ( T2 `2 = {} implies T1 `2 = {} ) & f is Function of (T1 `2),(T2 `2) & ( for x, y being set st [x,y] in T1 `1 holds
[(f . x),(f . y)] in T2 `1 ) )
by Th40;
[[T1,T2],f] `2 = f
;
hence
( m `2 is Function-like & m `2 is Relation-like )
by W; verum