deffunc H₁( Element of Fin I) -> Element of L = Sum (x,$1);
A3: for a, b being Function of (Fin I), the carrier of L st ( for q being Element of Fin I holds a . q = H₁(q) ) & ( for q being Element of Fin I holds b . q = H₁(q) ) holds
a = b from BINOP_2:sch 1();
let f, g be Function of ([#] (OrderedFIN I)), the carrier of L; :: thesis: ( ( for j being Element of Fin I holds f . j = Sum (x,j) ) & ( for j being Element of Fin I holds g . j = Sum (x,j) ) implies f = g )
assume that
A4: for j being Element of Fin I holds f . j = Sum (x,j) and
A5: for j being Element of Fin I holds g . j = Sum (x,j) ; :: thesis: f = g
the carrier of (OrderedFIN I) = Fin I by YELLOW_1:1;
then [#] (OrderedFIN I) = Fin I by STRUCT_0:def 3;
then reconsider f = f, g = g as Function of (Fin I), the carrier of L ;
f = g by A3, A4, A5;
hence f = g ; :: thesis: verum