let S1, S2 be SetSequence of ExtREAL; :: thesis: ( ( for n being Nat holds S1 . n = [.(b + n),+infty.] ) & ( for n being Nat holds S2 . n = [.(b + n),+infty.] ) implies S1 = S2 )
assume that
A4: for n being Nat holds S1 . n = [.(b + n),+infty.] and
A5: for n being Nat holds S2 . n = [.(b + n),+infty.] ; :: thesis: S1 = S2
for n being Element of NAT holds S1 . n = S2 . n

proof

let n be Element of NAT ; :: thesis: S1 . n = S2 . n
thus S1 . n = [.(b + n),+infty.] by A4
.= S2 . n by A5 ; :: thesis: verum

end;

hence S1 = S2 ; :: thesis: verum