let K be Field; :: thesis: ( 1. K,0 = 0. K,0 & 1. K,0 = {} )
A1:
( len (1. K,0 ) = 0 & width (1. K,0 ) = 0 )
by MATRIX_1:25;
len (0. K,0 ) = 0
by MATRIX_1:25;
then
0. K,0 = {}
;
hence
1. K,0 = 0. K,0
by A1; :: thesis: 1. K,0 = {}
thus
1. K,0 = {}
by A1; :: thesis: verum