= Balanced parentheses in propositional syntax
{title2=$L(\varphi)=R(\varphi)$}
Every <propositional formula> generated by a parenthesized grammar has equally many opening and closing parentheses. By <structural induction>, atomic formulas begin with equal zero counts; <negation> preserves them; and a parenthesized binary <logical connective> adds its two subformula counts and one parenthesis of each kind. An optional paired-parenthesis construction also adds one to both counts. This necessary syntactic invariant is useful for checking generated expressions, though equal counts alone do not guarantee correctly nested syntax.
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