Let $(X,F,\tau)$ be a probabilistic metric space. Is this inequality true?
$$l^-inf_{x\in X}\tau(F_n,G_n)\geq \tau(l^-inf_{x\in X} F_n,l^-inf_{x\in X} G_n)$$
Where $F_n,G_n$ are sequences of distribution functions in $\Delta^+$, $\tau$ is a continuous triangle function. (continuity of $\tau$ means continuity with respect to the weak topology on $\Delta^+$). and $l^-f(x)$ denote the left limit of function $f$.
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