statement stringlengths 1 4.33k | proof stringlengths 0 37.9k | type stringclasses 25
values | symbolic_name stringlengths 1 67 | library stringclasses 10
values | filename stringclasses 112
values | imports listlengths 2 138 | deps listlengths 0 64 | docstring stringclasses 798
values | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
comp_is_nondecreasing : nondecreasing (f \o g). | Proof. by move=> ? ? ?; do 2 apply: omorph_le. Qed. | Fact | comp_is_nondecreasing | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"apply",
"nondecreasing",
"omorph_le"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
val | := (val : U -> T). | Notation | val | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
leEsub x y : (x <= y) = (val x <= val y). | Proof. by rewrite le_val. Qed. | Lemma | leEsub | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"val"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lt_val : {mono val : x y / x < y}. | Proof. by move=> x y; rewrite !lt_leAnge !le_val. Qed. | Lemma | lt_val | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"lt_leAnge",
"val"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltEsub x y : (x < y) = (val x < val y). | Proof. by rewrite lt_val. Qed. | Lemma | ltEsub | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"lt_val",
"val"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
le_wval : {homo val : x y / x <= y}. | Proof. exact/mono2W/le_val. Qed. | Lemma | le_wval | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"val"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lt_wval : {homo val : x y / x < y}. | Proof. exact/mono2W/lt_val. Qed. | Lemma | lt_wval | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"lt_val",
"val"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
valD : order_morphism (val : U -> T). | Proof. by []. Qed. | Fact | valD | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"order_morphism",
"val"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"[ 'SubChoice_isSubPreorder' 'of' U 'by' <: ]" | :=
(SubChoice_isSubPreorder.Build _ _ _ _ U)
(at level 0, format "[ 'SubChoice_isSubPreorder' 'of' U 'by' <: ]")
: form_scope. | Notation | [ 'SubChoice_isSubPreorder' 'of' U 'by' <: ] | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"Build"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"[ 'SubChoice_isSubPreorder' 'of' U 'by' <: 'with' disp ]" | :=
(SubChoice_isSubPreorder.Build _ _ _ disp U)
(at level 0, format "[ 'SubChoice_isSubPreorder' 'of' U 'by' <: 'with' disp ]")
: form_scope. | Notation | [ 'SubChoice_isSubPreorder' 'of' U 'by' <: 'with' disp ] | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"Build"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat_display : disp_t. | Proof. exact. Qed. | Fact | nat_display | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"disp_t"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltn_def x y : (x < y)%N = (x <= y)%N && ~~ (y <= x)%N. | Proof. by rewrite -ltnNge andbC; case: (ltnP x y) => //= /ltnW. Qed. | Lemma | ltn_def | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"ltnNge",
"ltnP",
"ltnW"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
leEnat : le = leq. | Proof. by []. Qed. | Lemma | leEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"le",
"leq"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltEnat : lt = ltn. | Proof. by []. Qed. | Lemma | ltEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"lt",
"ltn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
minEnat : min = minn. | Proof. by []. Qed. | Lemma | minEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"min",
"minn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
maxEnat : max = maxn. | Proof. by []. Qed. | Lemma | maxEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"max",
"maxn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
botEnat : \bot = 0%N :> nat. | Proof. by []. Qed. | Lemma | botEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"bot",
"nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
leEnat | := leEnat. | Definition | leEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltEnat | := ltEnat. | Definition | ltEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
minEnat | := minEnat. | Definition | minEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
maxEnat | := maxEnat. | Definition | maxEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
botEnat | := botEnat. | Definition | botEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
homo_ltn_lt_in : {in D, forall i, i.+1 \in D -> f i < f i.+1} ->
{in D &, {homo f : i j / i < j}}. | Proof. by apply: homo_ltn_in Dconvex; apply: lt_trans. Qed. | Lemma | homo_ltn_lt_in | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"Dconvex",
"apply",
"homo_ltn_in",
"lt_trans"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nondecn_inP : {in D, forall i, i.+1 \in D -> f i <= f i.+1} ->
{in D &, {homo f : i j / i <= j}}. | Proof. by apply: homo_leq_in Dconvex => //; apply: le_trans. Qed. | Lemma | nondecn_inP | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"Dconvex",
"apply",
"homo_leq_in",
"le_trans"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nhomo_ltn_lt_in : {in D, forall i, i.+1 \in D -> f i > f i.+1} ->
{in D &, {homo f : i j /~ i < j}}. | Proof.
move=> f_dec; apply: homo_sym_in.
by apply: homo_ltn_in Dconvex f_dec => ? ? ? ? /lt_trans->.
Qed. | Lemma | nhomo_ltn_lt_in | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"Dconvex",
"apply",
"homo_ltn_in",
"lt_trans"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nonincn_inP : {in D, forall i, i.+1 \in D -> f i >= f i.+1} ->
{in D &, {homo f : i j /~ i <= j}}. | Proof.
move=> /= f_dec; apply: homo_sym_in.
by apply: homo_leq_in Dconvex f_dec => //= ? ? ? ? /le_trans->.
Qed. | Lemma | nonincn_inP | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"Dconvex",
"apply",
"homo_leq_in",
"le_trans"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
homo_ltn_lt : (forall i, f i < f i.+1) -> {homo f : i j / i < j}. | Proof. by apply: homo_ltn; apply: lt_trans. Qed. | Lemma | homo_ltn_lt | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"apply",
"homo_ltn",
"lt_trans"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nondecnP : (forall i, f i <= f i.+1) -> {homo f : i j / i <= j}. | Proof. by apply: homo_leq => //; apply: le_trans. Qed. | Lemma | nondecnP | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"apply",
"homo_leq",
"le_trans"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nhomo_ltn_lt : (forall i, f i > f i.+1) -> {homo f : i j /~ i < j}. | Proof.
move=> f_dec; apply: homo_sym.
by apply: homo_ltn f_dec => ? ? ? ? /lt_trans->.
Qed. | Lemma | nhomo_ltn_lt | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"apply",
"homo_ltn",
"lt_trans"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nonincnP : (forall i, f i >= f i.+1) -> {homo f : i j /~ i <= j}. | Proof.
move=> /= f_dec; apply: homo_sym.
by apply: homo_leq f_dec => //= ? ? ? ? /le_trans->.
Qed. | Lemma | nonincnP | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"apply",
"homo_leq",
"le_trans"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
dvd_display : disp_t. | Proof. exact. Qed. | Fact | dvd_display | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"disp_t"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
dvd | := (@le dvd_display _). | Notation | dvd | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"dvd_display",
"le"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"@ 'dvd' T" | := (@le dvd_display T)
(at level 10, T at level 8, only parsing) : function_scope. | Notation | @ 'dvd' T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"dvd_display",
"le"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sdvd | := (@lt dvd_display _). | Notation | sdvd | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"dvd_display",
"lt"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"@ 'sdvd' T" | := (@lt dvd_display T)
(at level 10, T at level 8, only parsing) : function_scope. | Notation | @ 'sdvd' T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"dvd_display",
"lt"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x %| y" | := (dvd x y) : order_scope. | Notation | x %| y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"dvd"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x %<| y" | := (sdvd x y) : order_scope. | Notation | x %<| y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sdvd"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat0 | := (@top dvd_display _). | Notation | nat0 | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"dvd_display",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat1 | := (@bottom dvd_display _). | Notation | nat1 | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"bottom",
"dvd_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
t | := nat. | Definition | t | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
dvdE : dvd = dvdn :> rel t. | Proof. by []. Qed. | Lemma | dvdE | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"dvd",
"dvdn",
"rel"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat1E : nat1 = 1%N :> t. | Proof. by []. Qed. | Lemma | nat1E | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"nat1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat0E : nat0 = 0%N :> t. | Proof. by []. Qed. | Lemma | nat0E | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"nat0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
natdvd | := t. | Notation | natdvd | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
dvdEnat | := dvdE. | Definition | dvdEnat | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"dvdE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat1E | := nat1E. | Definition | nat1E | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat0E | := nat0E. | Definition | nat0E | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ord_display : disp_t. | Proof. exact. Qed. | Fact | ord_display | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"disp_t"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
leEord : (le : rel 'I_n) = leq. | Proof. by []. Qed. | Lemma | leEord | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"le",
"leq",
"rel"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltEord : (lt : rel 'I_n) = (fun m n => m < n)%N. | Proof. by []. Qed. | Lemma | ltEord | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"lt",
"rel"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
botEord : \bot = ord0. | Proof. by []. Qed. | Lemma | botEord | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"bot",
"ord0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
topEord : \top = ord_max. | Proof. by []. Qed. | Lemma | topEord | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"ord_max",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
leEord | := leEord. | Definition | leEord | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltEord | := ltEord. | Definition | ltEord | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
botEord | := botEord. | Definition | botEord | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
topEord | := topEord. | Definition | topEord | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
bool_display : disp_t. | Proof. exact. Qed. | Fact | bool_display | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"disp_t"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltn_def x y : (x < y)%N = (x <= y)%N && ~~ (y <= x)%N. | Proof. by case: x y => [] []. Qed. | Fact | ltn_def | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
leEbool : le = (leq : rel bool). | Proof. by []. Qed. | Lemma | leEbool | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"le",
"leq",
"rel"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltEbool x y : (x < y) = (x < y)%N. | Proof. by []. Qed. | Lemma | ltEbool | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prod_display_unit (_ _ : unit) : unit. | Proof. exact: tt. Qed. | Fact | prod_display_unit | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"unit"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prod_display (displ dispr : disp_t) : disp_t | :=
Disp (prod_display_unit (d1 displ) (d1 dispr))
(prod_display_unit (d2 displ) (d2 dispr)). | Definition | prod_display | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"disp_t",
"prod_display_unit"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
seqprod_display (disp : disp_t) : disp_t. | Proof. exact: disp. Qed. | Fact | seqprod_display | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"disp_t"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<=^p%O" | := (@le (prod_display _ _) _) : function_scope. | Notation | <=^p%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"le",
"prod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=^p%O" | := (@ge (prod_display _ _) _) : function_scope. | Notation | >=^p%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"ge",
"prod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<^p%O" | := (@lt (prod_display _ _) _) : function_scope. | Notation | <^p%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"lt",
"prod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">^p%O" | := (@gt (prod_display _ _) _) : function_scope. | Notation | >^p%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"gt",
"prod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<?=^p%O" | := (@leif (prod_display _ _) _) : function_scope. | Notation | <?=^p%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"leif",
"prod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=<^p%O" | := (@comparable (prod_display _ _) _) : function_scope. | Notation | >=<^p%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"comparable",
"prod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"><^p%O" | := (fun x y => ~~ (@comparable (prod_display _ _) _ x y)) :
function_scope. | Notation | ><^p%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"comparable",
"prod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<=^p y" | := (>=^p%O y) : order_scope. | Notation | <=^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<=^p y :> T" | := (<=^p (y : T)) (only parsing) : order_scope. | Notation | <=^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=^p y" | := (<=^p%O y) : order_scope. | Notation | >=^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=^p y :> T" | := (>=^p (y : T)) (only parsing) : order_scope. | Notation | >=^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<^p y" | := (>^p%O y) : order_scope. | Notation | <^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<^p y :> T" | := (<^p (y : T)) (only parsing) : order_scope. | Notation | <^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">^p y" | := (<^p%O y) : order_scope. | Notation | >^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">^p y :> T" | := (>^p (y : T)) (only parsing) : order_scope. | Notation | >^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^p y" | := (<=^p%O x y) : order_scope. | Notation | x <=^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^p y :> T" | := ((x : T) <=^p (y : T)) (only parsing) : order_scope. | Notation | x <=^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >=^p y" | := (y <=^p x) (only parsing) : order_scope. | Notation | x >=^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >=^p y :> T" | := ((x : T) >=^p (y : T)) (only parsing) : order_scope. | Notation | x >=^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <^p y" | := (<^p%O x y) : order_scope. | Notation | x <^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <^p y :> T" | := ((x : T) <^p (y : T)) (only parsing) : order_scope. | Notation | x <^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >^p y" | := (y <^p x) (only parsing) : order_scope. | Notation | x >^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >^p y :> T" | := ((x : T) >^p (y : T)) (only parsing) : order_scope. | Notation | x >^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^p y <=^p z" | := ((x <=^p y) && (y <=^p z)) : order_scope. | Notation | x <=^p y <=^p z | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <^p y <=^p z" | := ((x <^p y) && (y <=^p z)) : order_scope. | Notation | x <^p y <=^p z | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^p y <^p z" | := ((x <=^p y) && (y <^p z)) : order_scope. | Notation | x <=^p y <^p z | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <^p y <^p z" | := ((x <^p y) && (y <^p z)) : order_scope. | Notation | x <^p y <^p z | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^p y ?= 'iff' C" | := (<?=^p%O x y C) : order_scope. | Notation | x <=^p y ?= 'iff' C | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^p y ?= 'iff' C :> T" | := ((x : T) <=^p (y : T) ?= iff C)
(only parsing) : order_scope. | Notation | x <=^p y ?= 'iff' C :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=<^p y" | := [pred x | >=<^p%O x y] : order_scope. | Notation | >=<^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=<^p y :> T" | := (>=<^p (y : T)) (only parsing) : order_scope. | Notation | >=<^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >=<^p y" | := (>=<^p%O x y) : order_scope. | Notation | x >=<^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"><^p y" | := [pred x | ~~ (>=<^p%O x y)] : order_scope. | Notation | ><^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"><^p y :> T" | := (><^p (y : T)) (only parsing) : order_scope. | Notation | ><^p y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x ><^p y" | := (~~ (><^p%O x y)) : order_scope. | Notation | x ><^p y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<=^sp%O" | := (@le (seqprod_display _) _) : function_scope. | Notation | <=^sp%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"le",
"seqprod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=^sp%O" | := (@ge (seqprod_display _) _) : function_scope. | Notation | >=^sp%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"ge",
"seqprod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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