let i be natural Number ; :: thesis: for r1, r2 being Real holds mlt ((i |-> r1),(i |-> r2)) = i |-> (r1 * r2)
let r1, r2 be Real; :: thesis: mlt ((i |-> r1),(i |-> r2)) = i |-> (r1 * r2)
reconsider s1 = r1, s2 = r2 as Element of REAL by XREAL_0:def 1;
mlt ((i |-> s1),(i |-> s2)) = s1 * (i |-> s2) by Th63
.= i |-> (r1 * r2) by Th48 ;
hence mlt ((i |-> r1),(i |-> r2)) = i |-> (r1 * r2) ; :: thesis: verum