let F, G be Membership_Func of C; :: thesis: ( ( for c being Element of C holds F . c = max ((h . c),(g . c)) ) & ( for c being Element of C holds G . c = max ((h . c),(g . c)) ) implies F = G )
assume that
A19: for c being Element of C holds F . c = max ((h . c),(g . c)) and
A20: for c being Element of C holds G . c = max ((h . c),(g . c)) ; :: thesis: F = G
A21: for c being Element of C st c in C holds
F . c = G . c

proof

let c be Element of C; :: thesis: ( c in C implies F . c = G . c )
F . c = max ((h . c),(g . c)) by A19;
hence ( c in C implies F . c = G . c ) by A20; :: thesis: verum

end;

( C = dom F & C = dom G ) by FUNCT_2:def 1;
hence F = G by A21, PARTFUN1:5; :: thesis: verum