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numbers.v: Don't Qed Decision instances

Merged Paolo G. Giarrusso requested to merge Blaisorblade/stdpp:paolo/qed-decision into master
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@@ -165,7 +165,8 @@ Module Nat.
Global Instance divide_dec : RelDecision Nat.divide.
Proof.
refine (λ x y, cast_if (decide (lcm x y = y))); by rewrite Nat.divide_lcm_iff.
refine (λ x y, cast_if (decide (lcm x y = y)));
abstract (by rewrite Nat.divide_lcm_iff).
Defined.
Global Instance divide_po : PartialOrder divide.
Proof.
@@ -1018,7 +1019,7 @@ Module Qp.
Global Instance eq_dec : EqDecision Qp.
Proof.
refine (λ p q, cast_if (decide (Qp_to_Qc p = Qp_to_Qc q)));
by rewrite <-to_Qc_inj_iff.
abstract (by rewrite <-to_Qc_inj_iff).
Defined.
Definition add (p q : Qp) : Qp :=
@@ -1063,13 +1064,13 @@ Module Qp.
Global Instance le_dec : RelDecision le.
Proof.
refine (λ p q, cast_if (decide (Qp_to_Qc p Qp_to_Qc q)%Qc));
by rewrite to_Qc_inj_le.
Qed.
abstract (by rewrite to_Qc_inj_le).
Defined.
Global Instance lt_dec : RelDecision lt.
Proof.
refine (λ p q, cast_if (decide (Qp_to_Qc p < Qp_to_Qc q)%Qc));
by rewrite to_Qc_inj_lt.
Qed.
abstract (by rewrite to_Qc_inj_lt).
Defined.
Global Instance lt_pi p q : ProofIrrel (lt p q).
Proof. destruct p, q; apply _. Qed.
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