let M1, M2 be Matrix of COMPLEX; :: thesis: ( len M1 = len M2 & width M1 = width M2 & M1 = M1 + M2 implies M2 = 0_Cx ((len M1),(width M1)) )
assume that
A1: ( len M1 = len M2 & width M1 = width M2 ) and
A2: M1 = M1 + M2 ; :: thesis: M2 = 0_Cx ((len M1),(width M1))
0_Cx ((len M1),(width M1)) = (M1 + M2) + (- M1) by A2, MATRIX_4:2
.= Field2COMPLEX (((COMPLEX2Field M2) + (COMPLEX2Field M1)) - (COMPLEX2Field M1)) by A1, MATRIX_3:2
.= M2 by A1, MATRIX_4:21 ;
hence M2 = 0_Cx ((len M1),(width M1)) ; :: thesis: verum