let D be non empty set ; :: thesis: for M1, M2 being Matrix of D st width M1 > 0 & width M2 > 0 & M1 @ = M2 @ holds
M1 = M2
let M1, M2 be Matrix of D; :: thesis: ( width M1 > 0 & width M2 > 0 & M1 @ = M2 @ implies M1 = M2 )
assume ( width M1 > 0 & width M2 > 0 ) ; :: thesis: ( not M1 @ = M2 @ or M1 = M2 )
then A1: ( width (M1 @) = len M1 & width (M2 @) = len M2 ) by Th54;
assume M1 @ = M2 @ ; :: thesis: M1 = M2
hence M1 = M2 by A1, Th53; :: thesis: verum