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Structural Induction on WFF For a formula α ∈ WFF we let l(α) denote the number...

Structural Induction on WFF

For a formula α ∈ WFF we let l(α) denote the number of symbols in α that are left brackets ‘(’, let v(α) the number of variable symbols, and c(α) the number of symbols that are the corner symbol ‘¬’. For example in ((p1 → p2) ∧ ((¬p1) → p2)) we have l(α) = 4, v(α) = 4 and c(α) = 1. Prove by induction that he following property holds for all well formed formulas:

• l(α)=v(α)+c(α)−1

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