lean2/tests/lean/run/class8.lean
Leonardo de Moura cbc81ea6c5 chore(*): minimize dependencies on tests
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
2014-08-24 19:58:48 -07:00

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import logic data.prod
using num tactic prod
inductive inh (A : Type) : Prop :=
inh_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 [instance] {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)
(*
print(get_env():find("T1"):value())
*)