fact stringlengths 8 1.54k | type stringclasses 19
values | library stringclasses 8
values | imports listlengths 1 10 | filename stringclasses 98
values | symbolic_name stringlengths 1 42 | docstring stringclasses 1
value |
|---|---|---|---|---|---|---|
rcomplEprodx y z :
rcompl x y z = (Order.rcompl x.1 y.1 z.1, Order.rcompl x.2 y.2 z.2).
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | rcomplEprod | |
Definition_ := CBDistrLattice.on T1'.
Let T2' : Type := T2.
HB.instance Definition _ := CBDistrLattice.on T2'. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
diffx y := (diff x.1 y.1, diff x.2 y.2).
#[export]
HB.instance Definition _ :=
@CDistrLattice_hasSectionalComplement.Build disp3 (T1 * T2)
diff (@diffErcompl _ _ T1' T2'). | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | diff | |
diffEprodx y : x `\` y = (x.1 `\` y.1, x.2 `\` y.2). Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | diffEprod | |
codiffx y := (codiff x.1 y.1, codiff x.2 y.2).
#[export]
HB.instance Definition _ :=
@CDistrLattice_hasDualSectionalComplement.Build disp3 (T1 * T2)
codiff (@diffErcompl _ _ T1^d T2^d). | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | codiff | |
codiffEprodx y :
codiff x y = (Order.codiff x.1 y.1, Order.codiff x.2 y.2).
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | codiffEprod | |
Definition_ := CTBDistrLattice.on T1'.
Let T2' : Type := T2.
HB.instance Definition _ := CTBDistrLattice.on T2'. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
complx := (~` x.1, ~` x.2).
#[export]
HB.instance Definition _ := @CDistrLattice_hasComplement.Build _ (T1 * T2) compl
(@complEdiff _ _ T1' T2') (@complEdiff _ _ T1^d T2^d). | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | compl | |
complEprodx : ~` x = (~` x.1, ~` x.2). Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | complEprod | |
Definition_ (T1 : finPOrderType disp1)
(T2 : finPOrderType disp2) := POrder.on (type disp3 T1 T2).
#[export]
HB.instance Definition _ (T1 : finBPOrderType disp1)
(T2 : finBPOrderType disp2) := POrder.on (type disp3 T1 T2).
#[export]
HB.instance Definition _ (T1 : finTPOrderType disp1)
(T2 : finTPOrderType disp2) ... | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
ltEprod:= @ltEprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | ltEprod | |
lt_pair:= @lt_pair. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | lt_pair | |
meetEprod:= @meetEprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | meetEprod | |
joinEprod:= @joinEprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | joinEprod | |
rcomplEprod:= @rcomplEprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | rcomplEprod | |
diffEprod:= @diffEprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | diffEprod | |
codiffEprod:= @codiffEprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | codiffEprod | |
complEprod:= @complEprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | complEprod | |
Definition_ (T1 : porderType disp1) (T2 : porderType disp2) :=
POrder.copy (T1 * T2)%type (prod T1 T2).
HB.instance Definition _ (T1 : bPOrderType disp1) (T2 : bPOrderType disp2) :=
BPOrder.copy (T1 * T2)%type (prod T1 T2).
HB.instance Definition _ (T1 : tPOrderType disp1) (T2 : tPOrderType disp2) :=
TPOrder.copy... | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
lex y := (tag x <= tag y) &&
((tag x >= tag y) ==> (tagged x <= tagged_as x y)). | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | le | |
ltx y := (tag x <= tag y) &&
((tag x >= tag y) ==> (tagged x < tagged_as x y)).
Fact refl : reflexive le.
Proof. by move=> [x x']; rewrite /le tagged_asE/= !lexx. Qed.
Fact anti : antisymmetric le.
Proof.
rewrite /le => -[x x'] [y y']/=; case: comparableP => //= eq_xy.
by case: _ / eq_xy in y' *; rewrite !tagged_asE ... | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | lt | |
leEsigx y : x <= y =
(tag x <= tag y) && ((tag x >= tag y) ==> (tagged x <= tagged_as x y)).
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | leEsig | |
ltEsigx y : x < y =
(tag x <= tag y) && ((tag x >= tag y) ==> (tagged x < tagged_as x y)).
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | ltEsig | |
le_Taggedlx (u : T' (tag x)) : (Tagged T' u <= x) = (u <= tagged x).
Proof. by case: x => [t v]/= in u *; rewrite leEsig/= lexx/= tagged_asE. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | le_Taggedl | |
le_Taggedrx (u : T' (tag x)) : (x <= Tagged T' u) = (tagged x <= u).
Proof. by case: x => [t v]/= in u *; rewrite leEsig/= lexx/= tagged_asE. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | le_Taggedr | |
lt_Taggedlx (u : T' (tag x)) : (Tagged T' u < x) = (u < tagged x).
Proof. by case: x => [t v]/= in u *; rewrite ltEsig/= lexx/= tagged_asE. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | lt_Taggedl | |
lt_Taggedrx (u : T' (tag x)) : (x < Tagged T' u) = (tagged x < u).
Proof. by case: x => [t v]/= in u *; rewrite ltEsig/= lexx/= tagged_asE. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | lt_Taggedr | |
Definition_ := hasBottom.Build _ {t : T & T' t} le0x. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
botEsig: \bot = Tagged T' (\bot : T' \bot). Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | botEsig | |
Definition_ := hasTop.Build _ {t : T & T' t} lex1. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
topEsig: \top = Tagged T' (\top : T' \top). Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | topEsig | |
Definition_ := POrder_isTotal.Build _ {t : T & T' t} total. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ (T : bOrderType disp1)
(T' : T -> bOrderType disp2) := POrder.on {t : T & T' t}.
#[export]
HB.instance Definition _ (T : tOrderType disp1)
(T' : T -> tOrderType disp2) := POrder.on {t : T & T' t}.
#[export]
HB.instance Definition _ (T : tbOrderType disp1)
(T' : T -> tbOrderType disp2) := POrder.on {t ... | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
leEsig:= @leEsig. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | leEsig | |
ltEsig:= @ltEsig. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | ltEsig | |
le_Taggedl:= @le_Taggedl. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | le_Taggedl | |
lt_Taggedl:= @lt_Taggedl. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | lt_Taggedl | |
le_Taggedr:= @le_Taggedr. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | le_Taggedr | |
lt_Taggedr:= @lt_Taggedr. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | lt_Taggedr | |
topEsig:= @topEsig. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | topEsig | |
botEsig:= @botEsig. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | botEsig | |
Definition_ := POrder.on T1'.
Let T2' : Type := T2.
HB.instance Definition _ := POrder.on T2'.
#[export]
HB.instance Definition _ :=
Preorder_isDuallyPOrder.Build disp3 (T1 * T2)
(@anti _ _ T1' T2') (@anti _ _ T1^d T2^d). | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ := POrder_isTotal.Build _ (T1 * T2) total. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ (T1 : finPOrderType disp1)
(T2 : finPOrderType disp2) := POrder.on (type disp3 T1 T2).
#[export]
HB.instance Definition _ (T1 : finBPOrderType disp1)
(T2 : finBPOrderType disp2) := POrder.on (type disp3 T1 T2).
#[export]
HB.instance Definition _ (T1 : finTPOrderType disp1)
(T2 : finTPOrderType disp2) ... | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ (T1 : porderType disp1) (T2 : porderType disp2) :=
POrder.copy (T1 * T2)%type (prodlexi T1 T2).
HB.instance Definition _ (T1 : orderType disp1) (T2 : orderType disp2) :=
Total.copy (T1 * T2)%type (prodlexi T1 T2).
HB.instance Definition _
(T1 : finPOrderType disp1) (T2 : finPOrderType disp2) :=
FinP... | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ := Preorder_isPOrder.Build disp' (seq T) anti. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
meets1 s2 :=
match s1, s2 with
| x1 :: s1', x2 :: s2' => (x1 `&` x2) :: meet s1' s2'
| _, _ => [::]
end.
Fact lexI s1 s2 s3 : (s1 <= meet s2 s3) = (s1 <= s2) && (s1 <= s3).
Proof.
elim: s1 s2 s3 => [|x s1 IHs1] [|y s2] [|z s3] //=; first by rewrite andbF.
by rewrite leEseq lexI IHs1 andbACA.
Qed.
#[export]
... | Fixpoint | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | meet | |
meetEseqs1 s2 : s1 `&` s2 = [seq x.1 `&` x.2 | x <- zip s1 s2].
Proof. by elim: s1 s2 => [|x s1 ihs1] [|y s2]//=; rewrite -ihs1. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | meetEseq | |
meet_consx1 s1 x2 s2 :
(x1 :: s1 : seq T) `&` (x2 :: s2) = (x1 `&` x2) :: s1 `&` s2.
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | meet_cons | |
joins1 s2 :=
match s1, s2 with
| [::], _ => s2 | _, [::] => s1
| x1 :: s1', x2 :: s2' => (x1 `|` x2) :: join s1' s2'
end.
Fact leUx s1 s2 s3 : (join s1 s2 <= s3) = (s1 <= s3) && (s2 <= s3).
Proof.
elim : s1 s2 s3 => [|x s1 IHs1] [|y s2] [|z s3] //=; first by rewrite andbT.
by rewrite leEseq leUx IHs1 andbAC... | Fixpoint | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | join | |
joinEseqs1 s2 : s1 `|` s2 =
match s1, s2 with
| [::], _ => s2 | _, [::] => s1
| x1 :: s1', x2 :: s2' => (x1 `|` x2) :: ((s1' : seq _) `|` s2')
end.
Proof. by case: s1. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | joinEseq | |
join_consx1 s1 x2 s2 :
(x1 :: s1 : seq T) `|` (x2 :: s2) = (x1 `|` x2) :: s1 `|` s2.
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | join_cons | |
Definition_ (T : latticeType disp) := POrder.on (seq T). | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ := Lattice_Meet_isDistrLattice.Build _ (seq T) meetUl. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
meetEseq:= @meetEseq. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | meetEseq | |
meet_cons:= @meet_cons. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | meet_cons | |
joinEseq:= @joinEseq. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | joinEseq | |
Definition_ (T : porderType disp) :=
POrder.copy (seq T) (seqprod T).
HB.instance Definition _ (T : meetSemilatticeType disp) :=
BMeetSemilattice.copy (seq T) (seqprod T).
HB.instance Definition _ (T : joinSemilatticeType disp) :=
BJoinSemilattice.copy (seq T) (seqprod T).
HB.instance Definition _ (T : latticeTyp... | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ := Preorder_isPOrder.Build disp' (seq T) anti. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
neqhead_lexiE(x y : T) s1 s2 : x != y ->
(x :: s1 <= y :: s2 :> seq _) = (x < y).
Proof. by rewrite lexi_cons; case: comparableP. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | neqhead_lexiE | |
neqhead_ltxiE(x y : T) s1 s2 : x != y ->
(x :: s1 < y :: s2 :> seq _) = (x < y).
Proof. by rewrite ltxi_cons; case: (comparableP x y). Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | neqhead_ltxiE | |
Definition_ := POrder_isTotal.Build _ (seq T) total. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
neqhead_lexiE:= @neqhead_lexiE. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | neqhead_lexiE | |
neqhead_ltxiE:= @neqhead_ltxiE. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | neqhead_ltxiE | |
Definition_ (T : porderType disp) :=
POrder.copy (seq T) (seqlexi T).
HB.instance Definition _ (T : orderType disp) :=
BTotal.copy (seq T) (seqlexi T). | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ n T := SubChoice.on (n.-tuple T).
#[export]
HB.instance Definition _ n T :=
[SubChoice_isSubPOrder of n.-tuple T by <: with disp']. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ (n : nat) (T : bPOrderType disp) :=
POrder.on (n.-tuple T). | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ (n : nat) (T : tPOrderType disp) :=
POrder.on (n.-tuple T).
#[export]
HB.instance Definition _ (n : nat) (T : tbPOrderType disp) :=
POrder.on (n.-tuple T). | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
meett1 t2 : n.-tuple T := [tuple tnth t1 i `&` tnth t2 i | i < n].
Fact lexI t1 t2 t3 : (t1 <= meet t2 t3) = (t1 <= t2) && (t1 <= t3).
Proof.
rewrite !leEtprod; apply/forallP/andP => [H|[Ht12 Ht13] i]; last first.
by rewrite tnth_mktuple lexI (forallP Ht12) (forallP Ht13).
by split; apply/forallP => i; move: (H i); r... | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | meet | |
tnth_meett1 t2 i : tnth (t1 `&` t2) i = tnth t1 i `&` tnth t2 i.
Proof. exact: tnth_mktuple. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_meet | |
meetEtprodt1 t2 : t1 `&` t2 = [tuple tnth t1 i `&` tnth t2 i | i < n].
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | meetEtprod | |
joint1 t2 : n.-tuple T := [tuple tnth t1 i `|` tnth t2 i | i < n].
Fact leUx t1 t2 t3 : (join t1 t2 <= t3) = (t1 <= t3) && (t2 <= t3).
Proof.
rewrite !leEtprod; apply/forallP/andP => [H|[Ht13 Ht23] i]; last first.
by rewrite tnth_mktuple leUx (forallP Ht13) (forallP Ht23).
by split; apply/forallP => i; move: (H i); r... | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | join | |
tnth_joint1 t2 i : tnth (t1 `|` t2) i = tnth t1 i `|` tnth t2 i.
Proof. exact: tnth_mktuple. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_join | |
joinEtprodt1 t2 : t1 `|` t2 = [tuple tnth t1 i `|` tnth t2 i | i < n].
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | joinEtprod | |
Definition_ (n : nat) (T : bMeetSemilatticeType disp) :=
POrder.on (n.-tuple T).
#[export]
HB.instance Definition _ (n : nat) (T : tMeetSemilatticeType disp) :=
POrder.on (n.-tuple T).
#[export]
HB.instance Definition _ (n : nat) (T : tbMeetSemilatticeType disp) :=
POrder.on (n.-tuple T).
#[export]
HB.instance De... | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ :=
Lattice_Meet_isDistrLattice.Build _ (n.-tuple T) meetUl. | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
Definition_ (n : nat) (T : bDistrLatticeType disp) :=
DistrLattice.on (n.-tuple T).
#[export]
HB.instance Definition _ (n : nat) (T : tDistrLatticeType disp) :=
DistrLattice.on (n.-tuple T).
#[export]
HB.instance Definition _ (n : nat) (T : tbDistrLatticeType disp) :=
DistrLattice.on (n.-tuple T). | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
rcomplt1 t2 t3 :=
[tuple rcompl (tnth t1 i) (tnth t2 i) (tnth t3 i) | i < n].
Fact rcomplPmeet x y z : ((x `&` y) `|` z) `&` rcompl x y z = x `&` y.
Proof. by apply: eq_from_tnth => i; rewrite !tnth_mktuple rcomplPmeet. Qed.
Fact rcomplPjoin x y z : ((y `|` x) `&` z) `|` rcompl x y z = y `|` x.
Proof. by apply: eq_fr... | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | rcompl | |
tnth_rcomplt1 t2 t3 i :
tnth (Order.rcompl t1 t2 t3) i =
Order.rcompl (tnth t1 i) (tnth t2 i) (tnth t3 i).
Proof. exact: tnth_mktuple. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_rcompl | |
rcomplEtprodt1 t2 t3 :
Order.rcompl t1 t2 t3 =
[tuple Order.rcompl (tnth t1 i) (tnth t2 i) (tnth t3 i) | i < n].
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | rcomplEtprod | |
difft1 t2 : n.-tuple T := [tuple tnth t1 i `\` tnth t2 i | i < n].
Fact diffErcompl t1 t2 : diff t1 t2 = rcompl \bot t1 t2.
Proof. by apply: eq_from_tnth => i; rewrite !tnth_mktuple diffErcompl. Qed.
#[export] HB.instance Definition _ :=
@CDistrLattice_hasSectionalComplement.Build _ (n.-tuple T) diff diffErcompl. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | diff | |
tnth_difft1 t2 i : tnth (diff t1 t2) i = tnth t1 i `\` tnth t2 i.
Proof. exact: tnth_mktuple. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_diff | |
diffEtprodt1 t2 : t1 `\` t2 = [tuple tnth t1 i `\` tnth t2 i | i < n].
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | diffEtprod | |
codifft1 t2 : n.-tuple T :=
[tuple Order.codiff (tnth t1 i) (tnth t2 i) | i < n].
Fact codiffErcompl t1 t2 : codiff t1 t2 = rcompl t1 \top t2.
Proof. by apply: eq_from_tnth => i; rewrite !tnth_mktuple codiffErcompl. Qed.
#[export] HB.instance Definition _ :=
@CDistrLattice_hasDualSectionalComplement.Build _ (n.-tup... | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | codiff | |
tnth_codifft1 t2 i :
tnth (Order.codiff t1 t2) i = Order.codiff (tnth t1 i) (tnth t2 i).
Proof. exact: tnth_mktuple. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_codiff | |
codiffEtprodt1 t2 :
Order.codiff t1 t2 = [tuple Order.codiff (tnth t1 i) (tnth t2 i) | i < n].
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | codiffEtprod | |
complt : n.-tuple T := map_tuple compl t.
Fact complEdiff t : compl t = (\top : n.-tuple T) `\` t.
Proof.
by apply: eq_from_tnth => i; rewrite tnth_map !tnth_mktuple complEdiff.
Qed.
Fact complEcodiff t : compl t = codiff (\bot : n.-tuple T) t.
Proof.
by apply: eq_from_tnth => i; rewrite tnth_map !tnth_mktuple complEco... | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | compl | |
tnth_complt i : tnth (~` t) i = ~` tnth t i.
Proof. by rewrite tnth_map. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_compl | |
complEtprodt : ~` t = map_tuple Order.compl t.
Proof. by []. Qed. | Lemma | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | complEtprod | |
Definition_ (n : nat) (T : finPOrderType disp) :=
POrder.on (n.-tuple T).
#[export]
HB.instance Definition _ (n : nat) (T : finBPOrderType disp) :=
POrder.on (n.-tuple T).
#[export]
HB.instance Definition _ (n : nat) (T : finTPOrderType disp) :=
POrder.on (n.-tuple T).
#[export]
HB.instance Definition _ (n : nat)... | HB.instance | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | Definition | |
tnth_meet:= @tnth_meet. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_meet | |
meetEtprod:= @meetEtprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | meetEtprod | |
tnth_join:= @tnth_join. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_join | |
joinEtprod:= @joinEtprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | joinEtprod | |
tnth_rcompl:= @tnth_rcompl. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_rcompl | |
rcomplEtprod:= @rcomplEtprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | rcomplEtprod | |
tnth_diff:= @tnth_diff. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_diff | |
diffEtprod:= @diffEtprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | diffEtprod | |
tnth_codiff:= @tnth_codiff. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | tnth_codiff | |
codiffEtprod:= @codiffEtprod. | Definition | order | [
"From HB Require Import structures",
"From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat choice seq",
"From mathcomp Require Import path fintype tuple bigop finset div prime finfun",
"From mathcomp Require Import finset",
"From mathcomp Require Export preorder"
] | order/order.v | codiffEtprod |
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