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) )
A1: (M1 + M2) + (- M2) = (M1 + M2) - M2 ;
assume ( len M1 = len M2 & width M1 = width M2 ) ; :: thesis: M1 = (M1 + M2) + (- M2)
hence M1 = (M1 + M2) + (- M2) by A1, Th21; :: thesis: verum