let n be Element of NAT ; :: thesis: for X being non empty addLoopStr
for seq being sequence of X holds (- seq) . n = - (seq . n)
let X be non empty addLoopStr ; :: thesis: for seq being sequence of X holds (- seq) . n = - (seq . n)
let seq be sequence of X; :: thesis: (- seq) . n = - (seq . n)
A1: dom (- seq) = NAT by FUNCT_2:def 1;
thus (- seq) . n = (- seq) /. n
.= - (seq /. n) by A1, VFUNCT_1:def 5
.= - (seq . n) ; :: thesis: verum