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removed some lemmas that have recently been included into mathcomp
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aleksnanevski committed Sep 23, 2024
1 parent 7ecce21 commit 5113278
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25 changes: 0 additions & 25 deletions examples/quicksort.v
Original file line number Diff line number Diff line change
Expand Up @@ -28,31 +28,6 @@ Local Open Scope order_scope.
(* but the development is repeated here to make the files *)
(* self-contained *)

Lemma perm_onC {T : finType} (S1 S2 : {set T}) (u1 u2 : {perm T}) :
perm_on S1 u1 ->
perm_on S2 u2 ->
[disjoint S1 & S2] ->
commute u1 u2.
Proof.
move=> pS1 pS2 S12; apply/permP => t; rewrite !permM.
case/boolP : (t \in S1) => tS1.
- have /[!disjoint_subset] /subsetP {}S12 := S12.
by rewrite !(out_perm pS2) //; apply: S12; rewrite // perm_closed.
case/boolP : (t \in S2) => tS2.
- have /[1!disjoint_sym] /[!disjoint_subset] /subsetP {}S12 := S12.
by rewrite !(out_perm pS1) //; apply: S12; rewrite // perm_closed.
by rewrite (out_perm pS1) // (out_perm pS2) // (out_perm pS1).
Qed.

Lemma tperm_on {T : finType} (x y : T) :
perm_on [set x; y] (tperm x y).
Proof.
apply/subsetP => z /[!inE]; case: tpermP => [->|->|];
by rewrite eqxx // orbT.
Qed.

(****)

Lemma leq_choose a b :
a < b ->
sumbool (a.+1 == b) (a.+1 < b).
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