let i be Nat; :: thesis: for c1, c2 being complex number holds (i |-> c1) - (i |-> c2) = i |-> (c1 - c2)
let c1, c2 be complex number ; :: thesis: (i |-> c1) - (i |-> c2) = i |-> (c1 - c2)
reconsider s1 = c1, s2 = c2 as Element of COMPLEX by XCMPLX_0:def 2;
(i |-> s1) - (i |-> s2) = i |-> (diffcomplex . s1,s2) by FINSEQOP:18
.= i |-> (c1 - c2) by BINOP_2:def 4 ;
hence (i |-> c1) - (i |-> c2) = i |-> (c1 - c2) ; :: thesis: verum