import logic data.prod open tactic prod inductive inh [class] (A : Type) : Prop := intro : A -> inh A instance inh.intro theorem inh_elim {A : Type} {B : Prop} (H1 : inh A) (H2 : A → B) : B := inh.rec H2 H1 theorem inh_exists {A : Type} {P : A → Prop} (H : ∃x, P x) : inh A := obtain w Hw, from H, inh.intro w theorem inh_bool [instance] : inh Prop := inh.intro true theorem inh_fun [instance] {A B : Type} (H : inh B) : inh (A → B) := inh.rec (λb, inh.intro (λa : A, b)) H theorem pair_inh [instance] {A : Type} {B : Type} (H1 : inh A) (H2 : inh B) : inh (prod A B) := inh_elim H1 (λa, inh_elim H2 (λb, inh.intro (pair a b))) definition assump := eassumption tactic_hint assump theorem tst {A B : Type} (H : inh B) : inh (A → B → B) theorem T1 {A B C D : Type} {P : C → Prop} (a : A) (H1 : inh B) (H2 : ∃x, P x) : inh ((A → A) × B × (D → C) × Prop) := have h1 [visible] : inh A, from inh.intro a, have h2 [visible] : inh C, from inh_exists H2, _ (* print(get_env():find("T1"):value()) *)