let K be Ring; :: thesis: for M1, M2 being Matrix of K st len M1 = len M2 & width M1 = width M2 holds
M1 = (M1 + M2) - M2
let M1, M2 be Matrix of K; :: thesis: ( len M1 = len M2 & width M1 = width M2 implies M1 = (M1 + M2) - M2 )
assume A1: ( len M1 = len M2 & width M1 = width M2 ) ; :: thesis: M1 = (M1 + M2) - M2
hence (M1 + M2) - M2 = M1 + (M2 - M2) by MATRIX_3:3
.= M1 by A1, Th20 ;
:: thesis: verum