20 lines
472 B
Text
20 lines
472 B
Text
import logic
|
|
open tactic
|
|
|
|
inductive inh [class] (A : Type) : Type :=
|
|
intro : A -> inh A
|
|
|
|
theorem inh_bool [instance] : inh Prop
|
|
:= inh.intro true
|
|
|
|
set_option elaborator.trace_instances true
|
|
|
|
theorem inh_fun [instance] {A B : Type} (H : inh B) : inh (A → B)
|
|
:= inh.rec (λ b, inh.intro (λ a : A, b)) H
|
|
|
|
theorem tst {A B : Type} (H : inh B) : inh (A → B → B)
|
|
|
|
theorem T1 {A : Type} (a : A) : inh A :=
|
|
by repeat [apply @inh.intro | eassumption]
|
|
|
|
theorem T2 : inh Prop
|