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Some cleaning in notation

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This commit is contained in:
Niels
2017-08-07 16:49:46 +02:00
parent 1bab2206a3
commit 1e373364b2
9 changed files with 136 additions and 137 deletions
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6
FiniteSets/representations/bad.v
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@@ -62,11 +62,11 @@ Module Export FSet.
comm x y #
uP x y px py = uP y x py px).
Variable (nlP : forall (x : FSet A) (px: P x),
nl x # uP E x eP px = px).
nl x # uP ∅ x eP px = px).
Variable (nrP : forall (x : FSet A) (px: P x),
nr x # uP x E px eP = px).
nr x # uP x ∅ px eP = px).
Variable (idemP : forall (x : A),
idem x # uP (L x) (L x) (lP x) (lP x) = lP x).
idem x # uP {|x|} {|x|} (lP x) (lP x) = lP x).
(* Induction principle *)
Fixpoint FSet_ind

31
FiniteSets/representations/definition.v
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@@ -33,7 +33,7 @@ Module Export FSet.
Axiom trunc : IsHSet FSet.
End FSet.
Arguments E {_}.
Arguments U {_} _ _.
Arguments L {_} _.
@@ -42,29 +42,32 @@ Module Export FSet.
Arguments nl {_} _.
Arguments nr {_} _.
Arguments idem {_} _.
Notation "{| x |}" := (L x).
Infix "∪" := U (at level 8, right associativity).
Notation "∅" := E.
Section FSet_induction.
Variable A: Type.
Variable (P : FSet A -> Type).
Variable (H : forall a : FSet A, IsHSet (P a)).
Variable (eP : P E).
Variable (lP : forall a: A, P (L a)).
Variable (uP : forall (x y: FSet A), P x -> P y -> P (U x y)).
Variable (H : forall X : FSet A, IsHSet (P X)).
Variable (eP : P ∅).
Variable (lP : forall a: A, P {|a|}).
Variable (uP : forall (x y: FSet A), P x -> P y -> P (x ∪ y)).
Variable (assocP : forall (x y z : FSet A)
(px: P x) (py: P y) (pz: P z),
assoc x y z #
(uP x (U y z) px (uP y z py pz))
(uP x (y ∪ z) px (uP y z py pz))
=
(uP (U x y) z (uP x y px py) pz)).
(uP (x ∪ y) z (uP x y px py) pz)).
Variable (commP : forall (x y: FSet A) (px: P x) (py: P y),
comm x y #
uP x y px py = uP y x py px).
Variable (nlP : forall (x : FSet A) (px: P x),
nl x # uP E x eP px = px).
nl x # uP ∅ x eP px = px).
Variable (nrP : forall (x : FSet A) (px: P x),
nr x # uP x E px eP = px).
nr x # uP x ∅ px eP = px).
Variable (idemP : forall (x : A),
idem x # uP (L x) (L x) (lP x) (lP x) = lP x).
idem x # uP {|x|} {|x|} (lP x) (lP x) = lP x).
(* Induction principle *)
Fixpoint FSet_ind
@@ -183,9 +186,11 @@ Module Export FSet.
End FSet_recursion.
Instance FSet_recursion A : HitRecursion (FSet A) := {
indTy := _; recTy := _;
H_inductor := FSet_ind A; H_recursor := FSet_rec A }.
Instance FSet_recursion A : HitRecursion (FSet A) :=
{
indTy := _; recTy := _;
H_inductor := FSet_ind A; H_recursor := FSet_rec A
}.
End FSet.