let H1, H2 be Functional_Sequence of D,REAL; :: thesis: ( ( for n being Nat holds H1 . n = abs (H . n) ) & ( for n being Nat holds H2 . n = abs (H . n) ) implies H1 = H2 )
assume that
A5: for n being Nat holds H1 . n = abs (H . n) and
A6: for n being Nat holds H2 . n = abs (H . n) ; :: thesis: H1 = H2

now

let n be Element of NAT ; :: thesis: H1 . n = H2 . n
H2 . n = abs (H . n) by A6;
hence H1 . n = H2 . n by A5; :: thesis: verum

end;

hence H1 = H2 by FUNCT_2:63; :: thesis: verum