let S, T be sequence of RNS; :: thesis: ( ( for n being Nat holds S . n = (S1 . n) - (S2 . n) ) & ( for n being Nat holds T . n = (S1 . n) - (S2 . n) ) implies S = T )
assume that
A2: for n being Nat holds S . n = (S1 . n) - (S2 . n) and
A3: for n being Nat holds T . n = (S1 . n) - (S2 . n) ; :: thesis: S = T
for n being Element of NAT holds S . n = T . n

proof

let n be Element of NAT ; :: thesis: S . n = T . n
S . n = (S1 . n) - (S2 . n) by A2;
hence S . n = T . n by A3; :: thesis: verum

end;

hence S = T by FUNCT_2:63; :: thesis: verum