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Some simplifications in proofs, extra proofs for implementation

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Niels
2017-08-07 15:39:01 +02:00
parent d5585f32c6
commit a0844f6be4
2 changed files with 43 additions and 67 deletions
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24
FiniteSets/implementations/interface.v
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@@ -94,15 +94,33 @@ Section properties.
auto.
Defined.
Hint Unfold set_eq set_subset.
Ltac simplify := intros ; autounfold in * ; apply reflect_eq ; reduce.
Definition well_defined_union : forall (A : Type) (X1 X2 Y1 Y2 : T A),
set_eq A X1 Y1 -> set_eq A X2 Y2 -> set_eq A (union X1 X2) (union Y1 Y2).
Proof.
simplify.
rewrite X, X0.
reflexivity.
Defined.
Definition well_defined_filter : forall (A : Type) (ϕ : A -> Bool) (X Y : T A),
set_eq A X Y -> set_eq A (filter ϕ X) (filter ϕ Y).
Proof.
simplify.
rewrite X0.
reflexivity.
Defined.
Variable (A : Type).
Context `{DecidablePaths A}.
Lemma union_comm : forall (X Y : T A),
set_eq A (union X Y) (union Y X).
Proof.
intros.
apply reflect_eq.
reduce.
simplify.
apply lattice_fset.
Defined.