Combination of parse-element-when-tree-match-induction-step-1, parse-element-when-tree-match-induction-step-2, parse-element-when-tree-match-induction-step-3, parse-element-when-tree-match-induction-step-4, and parse-element-when-tree-match-induction-step-5.
Theorem:
(defthm parse-element-when-tree-match-induction-step-1+2+3+4+5 (implies (and (mv-nth 0 (parse-rulename input)) (mv-nth 0 (parse-group input)) (pred-group input) (pred-option input)) (pred-element input)))