set M = the Probability of S;

set F = {1} --> the Probability of S;

for x being set st x in dom ({1} --> the Probability of S) holds

ex P being Probability of S st ({1} --> the Probability of S) . x = P by FUNCOP_1:7;

hence ex b_{1} being Function st b_{1} is S -Probability_valued
by Def4; :: thesis: verum

set F = {1} --> the Probability of S;

for x being set st x in dom ({1} --> the Probability of S) holds

ex P being Probability of S st ({1} --> the Probability of S) . x = P by FUNCOP_1:7;

hence ex b