let N, n be Nat; :: thesis: for seq being Real_Sequence of N holds (- seq) . n = - (seq . n)
let seq be Real_Sequence of N; :: thesis: (- seq) . n = - (seq . n)
reconsider m = n as Element of NAT by ORDINAL1:def 12;
A1: dom (- seq) = NAT by FUNCT_2:def 1;
thus (- seq) . n = (- seq) /. m
.= - (seq /. m) by A1, VFUNCT_1:def 5
.= - (seq . n) ; :: thesis: verum