let M1, M2 be Matrix of COMPLEX; :: thesis: ( len M1 = len M2 & width M1 = width M2 & M1 + M2 = 0_Cx ((len M1),(width M1)) implies M2 = - M1 )
assume that
A1: ( len M1 = len M2 & width M1 = width M2 ) and
A2: M1 + M2 = 0_Cx ((len M1),(width M1)) ; :: thesis: M2 = - M1
A3: ( 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 A2, MATRIX_4:1;
then COMPLEX2Field M1 = - (COMPLEX2Field M2) by A1, A3, MATRIX_4:7;
hence M2 = - M1 by MATRIX_4:1; :: thesis: verum