let n be Element of NAT ; :: thesis: for K being Field
for M1, M2, M3 being Matrix of n,K st M1 is col_circulant & M2 is col_circulant & M3 is col_circulant holds
(M1 + M2) + M3 is col_circulant
let K be Field; :: thesis: for M1, M2, M3 being Matrix of n,K st M1 is col_circulant & M2 is col_circulant & M3 is col_circulant holds
(M1 + M2) + M3 is col_circulant
let M1, M2, M3 be Matrix of n,K; :: thesis: ( M1 is col_circulant & M2 is col_circulant & M3 is col_circulant implies (M1 + M2) + M3 is col_circulant )
assume that
A1: ( M1 is col_circulant & M2 is col_circulant ) and
A2: M3 is col_circulant ; :: thesis: (M1 + M2) + M3 is col_circulant
M1 + M2 is col_circulant by A1, Th21;
hence (M1 + M2) + M3 is col_circulant by A2, Th21; :: thesis: verum