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Remove the few instances of non-global hint declarations. #126

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Apr 7, 2024
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Remove the few instances of non-global hint declarations. #126

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9 changes: 6 additions & 3 deletions theory/cut_minus.v
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Expand Up @@ -12,7 +12,8 @@ Section cut_minus_properties.
Local Existing Instance pseudo_srorder_semiring.

Add Ring SR: (rings.stdlib_semiring_theory R).
Hint Resolve (@orders.le_flip R _ _).
Let local_le_flip := @orders.le_flip R _ _.
Hint Resolve local_le_flip.

Global Instance cut_minus_proper: Proper ((=) ==> (=) ==> (=)) cut_minus | 1.
Proof.
Expand All @@ -30,8 +31,10 @@ Section cut_minus_properties.
Global Instance cut_minus_mor_2: ∀ x : R, Setoid_Morphism (∸ x) | 0.
Proof. split; try apply _. solve_proper. Qed.

Hint Resolve (cut_minus_0).
Hint Resolve (cut_minus_le).
Let local_cut_minus_0 := (cut_minus_0).
Let local_cut_minus_le := (cut_minus_le).
Hint Resolve local_cut_minus_0.
Hint Resolve local_cut_minus_le.

Lemma cut_minus_diag x : x ∸ x = 0.
Proof. now apply cut_minus_0. Qed.
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6 changes: 5 additions & 1 deletion theory/ring_ideals.v
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Expand Up @@ -20,8 +20,12 @@ Section ideal_congruence.
Context `{ideal : RingIdeal A P}.
Add Ring A2 : (rings.stdlib_ring_theory A).

Let local_ideal_closed_plus_negate := (ideal_closed_plus_negate).
Let local_ideal_closed_mult_l := (ideal_closed_mult_l).
Let local_ideal_closed_mult_r := (ideal_closed_mult_r).

(* If P is an ideal, we can easily derive some further closedness properties: *)
Hint Resolve (ideal_closed_plus_negate) (ideal_closed_mult_l) (ideal_closed_mult_r).
Hint Resolve local_ideal_closed_plus_negate local_ideal_closed_mult_l local_ideal_closed_mult_r.

Lemma ideal_closed_0 : P 0.
Proof. destruct ideal_NonEmpty as [[x Px]]. rewrite <-(plus_negate_r x). intuition. Qed.
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