take s = len p; :: according to ALGSEQ_1:def 1 :: thesis: for b₁ being set holds
( not s <= b₁ or (- p) . b₁ = 0. L )
let i be Nat; :: thesis: ( not s <= i or (- p) . i = 0. L )
assume A1: i >= s ; :: thesis: (- p) . i = 0. L
thus (- p) . i = - (p . i) by BHSP_1:44
.= - (0. L) by A1, ALGSEQ_1:8
.= 0. L by RLVECT_1:12 ; :: thesis: verum