let M1, M2 be Matrix of COMPLEX ; :: thesis: ( len M1 = len M2 & width M1 = width M2 & len M1 > 0 & M1 + M2 = 0_Cx (len M1),(width M1) implies M2 = - M1 )
assume A1: ( len M1 = len M2 & width M1 = width M2 & len M1 > 0 & M1 + M2 = 0_Cx (len M1),(width M1) ) ; :: thesis: M2 = - M1
A2: ( len (- M2) = len M2 & width (- M2) = width M2 ) by MATRIX_3:def 2;
COMPLEX2Field (0_Cx (len M1),(width M1)) = (COMPLEX2Field M1) - (- (COMPLEX2Field M2)) by A1, MATRIX_4:1;
then COMPLEX2Field M1 = - (COMPLEX2Field M2) by A1, A2, MATRIX_4:7;
hence M2 = - M1 by MATRIX_4:1; :: thesis: verum