let p be Element of REAL 3; p = <*(p . 1),(p . 2),(p . 3)*>
consider x, y, z being Element of REAL such that
A1:
p = <*x,y,z*>
by FINSEQ_2:123;
<*x,y,z*> =
<*(p . 1),y,z*>
by A1, FINSEQ_1:62
.=
<*(p . 1),(p . 2),z*>
by A1, FINSEQ_1:62
.=
<*(p . 1),(p . 2),(p . 3)*>
by A1, FINSEQ_1:62
;
hence
p = <*(p . 1),(p . 2),(p . 3)*>
by A1; verum