# if F , G are two formulas , h[f] is the height of the formula f ,then h[ G a F ] is less or equal to sup( h[F] , h[G] ) + 1

if F , G are two propostional formulas , h[f] is the height of the formula f ,

then h[ G a F ] is less or equal to sup( h[F] , h[G] ) + 1 , a is one of the connectives , my question is , what is sup ??? and how to compute sup ?!!

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$\sup$ is most likely the supremum:
The term $\sup$ stands for supremum. For finite sets, it coincides with $\max$, the maximum. So for example $\sup(3,7)=7$, and $\sup(4,4)=4$. It is surprising that $\sup$ was used instead of the more common $\max$.