let S, T be sequence of RNS; ( ( 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)
; S = T
for n being Element of NAT holds S . n = T . n
hence
S = T
by FUNCT_2:63; verum