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Some cleaning in list representation

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This commit is contained in:
Niels van der Weide
2017-09-26 11:56:58 +02:00
parent 0e9fcbc588
commit d7a95697fb
3 changed files with 34 additions and 17 deletions
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21
FiniteSets/list_representation/list_representation.v
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@@ -79,6 +79,27 @@ Module Export FSetC.
indTy := _; recTy := _;
H_inductor := FSetC_ind A; H_recursor := FSetC_rec A
}.
Section FSetC_prim_recursion.
Variable (A : Type)
(P : Type)
(H : IsHSet P)
(nil : P)
(cns : A -> FSetC A -> P -> P)
(duplP : forall (a : A) (X : FSetC A) (x : P),
cns a (a ;; X) (cns a X x) = (cns a X x))
(commP : forall (a b: A) (X : FSetC A) (x: P),
cns a (b ;; X) (cns b X x) = cns b (a ;; X) (cns a X x)).
(* Recursion principle *)
Definition FSetC_prim_rec : FSetC A -> P.
Proof.
simple refine (FSetC_ind A (fun _ => P) (fun _ => H) nil cns _ _ );
try (intros; simple refine ((transport_const _ _) @ _ )); cbn.
- apply duplP.
- apply commP.
Defined.
End FSetC_prim_recursion.
End FSetC.
Infix ";;" := Cns (at level 8, right associativity).