let Omega be non empty set ; :: thesis: for Sigma being SigmaField of Omega

for A, B being Event of Sigma

for P being Probability of Sigma holds P . (A \/ B) <= (P . A) + (P . B)

let Sigma be SigmaField of Omega; :: thesis: for A, B being Event of Sigma

for P being Probability of Sigma holds P . (A \/ B) <= (P . A) + (P . B)

let A, B be Event of Sigma; :: thesis: for P being Probability of Sigma holds P . (A \/ B) <= (P . A) + (P . B)

let P be Probability of Sigma; :: thesis: P . (A \/ B) <= (P . A) + (P . B)

( 0 <= P . (A /\ B) & P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B)) ) by Def8, Th38;

hence P . (A \/ B) <= (P . A) + (P . B) by XREAL_1:43; :: thesis: verum

for A, B being Event of Sigma

for P being Probability of Sigma holds P . (A \/ B) <= (P . A) + (P . B)

let Sigma be SigmaField of Omega; :: thesis: for A, B being Event of Sigma

for P being Probability of Sigma holds P . (A \/ B) <= (P . A) + (P . B)

let A, B be Event of Sigma; :: thesis: for P being Probability of Sigma holds P . (A \/ B) <= (P . A) + (P . B)

let P be Probability of Sigma; :: thesis: P . (A \/ B) <= (P . A) + (P . B)

( 0 <= P . (A /\ B) & P . (A \/ B) = ((P . A) + (P . B)) - (P . (A /\ B)) ) by Def8, Th38;

hence P . (A \/ B) <= (P . A) + (P . B) by XREAL_1:43; :: thesis: verum