let n be Element of NAT ; :: thesis: for K being Field
for M1, M2, M3 being Matrix of n,K st M1 is line_circulant & M2 is line_circulant & M3 is line_circulant holds
(M1 + M2) + M3 is line_circulant
let K be Field; :: thesis: for M1, M2, M3 being Matrix of n,K st M1 is line_circulant & M2 is line_circulant & M3 is line_circulant holds
(M1 + M2) + M3 is line_circulant
let M1, M2, M3 be Matrix of n,K; :: thesis: ( M1 is line_circulant & M2 is line_circulant & M3 is line_circulant implies (M1 + M2) + M3 is line_circulant )
assume that
A1: ( M1 is line_circulant & M2 is line_circulant ) and
A2: M3 is line_circulant ; :: thesis: (M1 + M2) + M3 is line_circulant
M1 + M2 is line_circulant by A1, Th7;
hence (M1 + M2) + M3 is line_circulant by A2, Th7; :: thesis: verum