lean2/examples/lean/ex2.lean

import macros.

theorem simple (p q r : Bool) : (p → q) ∧ (q → r) → p → r
:= λ H_pq_qr H_p,
     let P_pq := and_eliml H_pq_qr,
         P_qr := and_elimr H_pq_qr
     in P_qr (P_pq H_p)

set_option pp::implicit true.
print environment 1.

theorem simple2 (a b c : Bool) : (a → b → c) → (a → b) → a → c
:= λ H_abc H_ab H_a,
     (H_abc H_a) (H_ab H_a)

print environment 1.