What is the meaning of the white space in the following notation (or what is meant by the rules themselves)?
$\frac{ }{x\ \ \ x}$
or
$\frac{y\ \ \ t_i}{y\ \ \ ft_1...t_n}$
Where the white space occurs between the variables in rule 1 and the variable and terms in rule two.
I'm self studying from Mathematical Logic by Ebbinghaus, Flum, and Thomas. This particular notation appears on page 23, in Exercise 4.6.
Further background. In a preface comment to Exercise 4.6, the book says: "A means of defining the preceding notions by calculi is indicated in the following exercise". The calculi is what I gave above, and the preceding notions are given below, where the function var "associates with each S-term the set of variables occuring in it":
$\operatorname{var}(x) :={x}$ $\operatorname{var}(c) := \emptyset$ $\operatorname{var}(ft_1 \ldots t_n):= \operatorname{var}(t_1)\cup \cdots \cup \operatorname{var}(t_n)$