let s1, s2 be Real_Sequence; :: thesis: ( ( for n being Element of NAT holds s1 . n = k to_power (seq . n) ) & ( for n being Element of NAT holds s2 . n = k to_power (seq . n) ) implies s1 = s2 )
assume that
A1: for n being Element of NAT holds s1 . n = k to_power (seq . n) and
A2: for n being Element of NAT holds s2 . n = k to_power (seq . n) ; :: thesis: s1 = s2
let n be Element of NAT ; :: according to FUNCT_2:def 8 :: thesis: K74(s1,n) = K74(s2,n)
thus s1 . n = k to_power (seq . n) by A1
.= s2 . n by A2 ; :: thesis: verum