let C1, C2 be Matrix of n,K; :: thesis: ( ( for i, j being Nat st [i,j] in Indices C1 holds
C1 * (i,j) = Cofactor (M,i,j) ) & ( for i, j being Nat st [i,j] in Indices C2 holds
C2 * (i,j) = Cofactor (M,i,j) ) implies C1 = C2 )
assume that
A1: for i, j being Nat st [i,j] in Indices C1 holds
C1 * (i,j) = Cofactor (M,i,j) and
A2: for i, j being Nat st [i,j] in Indices C2 holds
C2 * (i,j) = Cofactor (M,i,j) ; :: thesis: C1 = C2

now :: thesis: for i, j being Nat st [i,j] in Indices C1 holds
C1 * (i,j) = C2 * (i,j)

A3: Indices C1 = Indices C2 by MATRIX_0:26;
let i, j be Nat; :: thesis: ( [i,j] in Indices C1 implies C1 * (i,j) = C2 * (i,j) )
assume A4: [i,j] in Indices C1 ; :: thesis: C1 * (i,j) = C2 * (i,j)
reconsider i9 = i, j9 = j as Element of NAT by ORDINAL1:def 12;
C1 * (i,j) = Cofactor (M,i9,j9) by A1, A4;
hence C1 * (i,j) = C2 * (i,j) by A2, A4, A3; :: thesis: verum

end;

hence C1 = C2 by MATRIX_0:27; :: thesis: verum