let i be natural Number ; :: thesis: for r1, r2 being Real holds (i |-> r1) - (i |-> r2) = i |-> (r1 - r2)
let r1, r2 be Real; :: thesis: (i |-> r1) - (i |-> r2) = i |-> (r1 - r2)
reconsider s1 = r1, s2 = r2 as Element of REAL by XREAL_0:def 1;
(i |-> s1) - (i |-> s2) = i |-> (diffreal . (s1,s2)) by FINSEQOP:17
.= i |-> (r1 - r2) by BINOP_2:def 10 ;
hence (i |-> r1) - (i |-> r2) = i |-> (r1 - r2) ; :: thesis: verum