34 lines
1,008 B
Text
34 lines
1,008 B
Text
|
/-
|
||
|
|
Copyright (c) 2015 Floris van Doorn. All rights reserved.
|
||
|
|
Released under Apache 2.0 license as described in the file LICENSE.
|
||
|
|
|
||
|
|
Module: hit.cylinder
|
||
|
|
Authors: Floris van Doorn
|
||
|
|
|
||
|
|
Mapping cylinders
|
||
|
|
-/
|
||
|
|
|
||
|
|
/- The hit mapping cylinder is primitive, declared in init.hit. -/
|
||
|
|
|
||
|
|
open eq
|
||
|
|
|
||
|
|
namespace cylinder
|
||
|
|
|
||
|
|
variables {A B : Type} {f : A → B}
|
||
|
|
|
||
|
|
protected definition elim {P : Type} (Pbase : B → P) (Ptop : A → P)
|
||
|
|
(Pseg : Π(a : A), Ptop a = Pbase (f a)) {b : B} (x : cylinder f b) : P :=
|
||
|
|
cylinder.rec Pbase Ptop (λa, !tr_constant ⬝ Pseg a) x
|
||
|
|
|
||
|
|
protected definition elim_on [reducible] {P : Type} {b : B} (x : cylinder f b)
|
||
|
|
(Pbase : B → P) (Ptop : A → P)
|
||
|
|
(Pseg : Π(a : A), Ptop a = Pbase (f a)) : P :=
|
||
|
|
cylinder.elim Pbase Ptop Pseg x
|
||
|
|
|
||
|
|
definition elim_seg {P : Type} (Pbase : B → P) (Ptop : A → P)
|
||
|
|
(Pseg : Π(a : A), Ptop a = Pbase (f a)) {b : B} (x : cylinder f b) (a : A) :
|
||
|
|
ap (elim Pbase Ptop Pseg) (seg f a) = sorry ⬝ Pseg a ⬝ sorry :=
|
||
|
|
sorry
|
||
|
|
|
||
|
|
end cylinder
|