let N be Element of NAT ; :: thesis: for seq being Real_Sequence of N holds 1 * seq = seq
let seq be Real_Sequence of N; :: thesis: 1 * seq = seq

now

let n be Element of NAT ; :: thesis: (1 * seq) . n = seq . n
thus (1 * seq) . n = 1 * (seq . n) by Def3
.= seq . n by EUCLID:33 ; :: thesis: verum

end;

hence 1 * seq = seq by FUNCT_2:113; :: thesis: verum