Two player-points P and E in the normed space B with convex vectogrammes V ⊂ U ⊂ B have antagonistic goals: E to reach a point of some set l named 'life line' before capture, P to prevent it. Capture is P(t) = E(t). Each goal function for the players has only two values 'winning' and 'loss'. The key for game analysis is safety zone A(t). The shrinkage of safety zones t₂ > t₁ ⇒ A(t₂) ⊂ A(t₁) is of principal importance. It is shown that P's strategy providing the shrinkage for every E's strategy also provides the capture in closure of A(0).