lean2/examples/lean/ex2.lean

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Theorem simple (p q r : Bool) : (p ⇒ q) ∧ (q ⇒ r) ⇒ p ⇒ r :=
Discharge (λ H_pq_qr, Discharge (λ H_p,
let P_pq := Conjunct1 H_pq_qr,
P_qr := Conjunct2 H_pq_qr,
P_q := MP P_pq H_p
in MP P_qr P_q))
Set pp::implicit true
Show Environment 1
Theorem simple2 (a b c : Bool) : (a ⇒ b ⇒ c) ⇒ (a ⇒ b) ⇒ a ⇒ c :=
Discharge (λ H_abc, Discharge (λ H_ab, Discharge (λ H_a,
let P_b := (MP H_ab H_a),
P_bc := (MP H_abc H_a)
in MP P_bc P_b)))
Show Environment 1