2014-07-27 19:17:38 +00:00
|
|
|
import logic
|
2014-09-05 01:41:06 +00:00
|
|
|
open eq
|
2014-07-27 19:17:38 +00:00
|
|
|
abbreviation subsets (P : Type) := P → Prop.
|
|
|
|
|
|
2014-09-06 18:05:07 +00:00
|
|
|
context
|
2014-07-27 19:17:38 +00:00
|
|
|
|
|
|
|
|
hypothesis A : Type.
|
|
|
|
|
|
|
|
|
|
hypothesis r : A → subsets A.
|
|
|
|
|
|
|
|
|
|
hypothesis i : subsets A → A.
|
|
|
|
|
|
|
|
|
|
hypothesis retract {P : subsets A} {a : A} : r (i P) a = P a.
|
|
|
|
|
|
|
|
|
|
definition delta (a:A) : Prop := ¬ (r a a).
|
|
|
|
|
|
|
|
|
|
notation `δ` := delta.
|
|
|
|
|
|
|
|
|
|
theorem delta_aux : ¬ (δ (i delta))
|
|
|
|
|
:= assume H : δ (i delta),
|
|
|
|
|
H (subst (symm retract) H).
|
|
|
|
|
|
2014-08-08 00:08:59 +00:00
|
|
|
check delta_aux.
|
|
|
|
|
|
2014-09-05 01:41:06 +00:00
|
|
|
end
|
