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 |
|---|---|---|---|---|---|---|---|---|---|---|
"<^sp%O" | := (@lt (seqprod_display _) _) : function_scope. | Notation | <^sp%O | order | order/preorder.v | [
"HB",
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"mathcomp",
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"ssrfun",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"lt",
"seqprod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">^sp%O" | := (@gt (seqprod_display _) _) : function_scope. | Notation | >^sp%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"gt",
"seqprod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<?=^sp%O" | := (@leif (seqprod_display _) _) : function_scope. | Notation | <?=^sp%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
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"ssrnat",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"leif",
"seqprod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=<^sp%O" | := (@comparable (seqprod_display _) _) : function_scope. | Notation | >=<^sp%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"comparable",
"seqprod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"><^sp%O" | := (fun x y => ~~ (@comparable (seqprod_display _) _ x y)) :
function_scope. | Notation | ><^sp%O | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"eqtype",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"comparable",
"seqprod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<=^sp y" | := (>=^sp%O y) : order_scope. | Notation | <=^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<=^sp y :> T" | := (<=^sp (y : T)) (only parsing) : order_scope. | Notation | <=^sp y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=^sp y" | := (<=^sp%O y) : order_scope. | Notation | >=^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
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"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=^sp y :> T" | := (>=^sp (y : T)) (only parsing) : order_scope. | Notation | >=^sp y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
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"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<^sp y" | := (>^sp%O y) : order_scope. | Notation | <^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<^sp y :> T" | := (<^sp (y : T)) (only parsing) : order_scope. | Notation | <^sp y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">^sp y" | := (<^sp%O y) : order_scope. | Notation | >^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
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"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">^sp y :> T" | := (>^sp (y : T)) (only parsing) : order_scope. | Notation | >^sp y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
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"ssrfun",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^sp y" | := (<=^sp%O x y) : order_scope. | Notation | x <=^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^sp y :> T" | := ((x : T) <=^sp (y : T)) (only parsing) : order_scope. | Notation | x <=^sp y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >=^sp y" | := (y <=^sp x) (only parsing) : order_scope. | Notation | x >=^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >=^sp y :> T" | := ((x : T) >=^sp (y : T)) (only parsing) : order_scope. | Notation | x >=^sp y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <^sp y" | := (<^sp%O x y) : order_scope. | Notation | x <^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
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"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <^sp y :> T" | := ((x : T) <^sp (y : T)) (only parsing) : order_scope. | Notation | x <^sp y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >^sp y" | := (y <^sp x) (only parsing) : order_scope. | Notation | x >^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
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"prime",
"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >^sp y :> T" | := ((x : T) >^sp (y : T)) (only parsing) : order_scope. | Notation | x >^sp y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^sp y <=^sp z" | := ((x <=^sp y) && (y <=^sp z)) : order_scope. | Notation | x <=^sp y <=^sp z | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <^sp y <=^sp z" | := ((x <^sp y) && (y <=^sp z)) : order_scope. | Notation | x <^sp y <=^sp z | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
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"eqtype",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^sp y <^sp z" | := ((x <=^sp y) && (y <^sp z)) : order_scope. | Notation | x <=^sp y <^sp z | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <^sp y <^sp z" | := ((x <^sp y) && (y <^sp z)) : order_scope. | Notation | x <^sp y <^sp z | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^sp y ?= 'iff' C" | := (<?=^sp%O x y C) : order_scope. | Notation | x <=^sp y ?= 'iff' C | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x <=^sp y ?= 'iff' C :> T" | := ((x : T) <=^sp (y : T) ?= iff C)
(only parsing) : order_scope. | Notation | x <=^sp y ?= 'iff' C :> T | order | order/preorder.v | [
"HB",
"structures",
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"ssrfun",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=<^sp y" | := [pred x | >=<^sp%O x y] : order_scope. | Notation | >=<^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=<^sp y :> T" | := (>=<^sp (y : T)) (only parsing) : order_scope. | Notation | >=<^sp y :> T | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x >=<^sp y" | := (>=<^sp%O x y) : order_scope. | Notation | x >=<^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
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"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"><^sp y" | := [pred x | ~~ (>=<^sp%O x y)] : order_scope. | Notation | ><^sp y | order | order/preorder.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
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"finfun",
"DvdSyntax",
"DefaultSeqProdOrder",
"DefaultSeqLexiOrder",
"SetSubsetOrder.Exports",
"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"><^sp y :> T" | := (><^sp (y : T)) (only parsing) : order_scope. | Notation | ><^sp y :> T | order | order/preorder.v | [
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"structures",
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"OrdinalOrd... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"x ><^sp y" | := (~~ (><^sp%O x y)) : order_scope. | Notation | x ><^sp 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... | [
"sp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lexi_display (disp _ : disp_t) : disp_t. | Proof. exact: disp. Qed. | Fact | lexi_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 | |
seqlexi_display (disp : disp_t) : disp_t. | Proof. exact: disp. Qed. | Fact | seqlexi_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 | |
"<=^l%O" | := (@le (lexi_display _ _) _) : function_scope. | Notation | <=^l%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",
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=^l%O" | := (@ge (lexi_display _ _) _) : function_scope. | Notation | >=^l%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",
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<^l%O" | := (@lt (lexi_display _ _) _) : function_scope. | Notation | <^l%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... | [
"lexi_display",
"lt"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">^l%O" | := (@gt (lexi_display _ _) _) : function_scope. | Notation | >^l%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",
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<?=^l%O" | := (@leif (lexi_display _ _) _) : function_scope. | Notation | <?=^l%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",
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=<^l%O" | := (@comparable (lexi_display _ _) _) : function_scope. | Notation | >=<^l%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",
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"><^l%O" | := (fun x y => ~~ (@comparable (lexi_display _ _) _ x y)) :
function_scope. | Notation | ><^l%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",
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<=^l y" | := (>=^l%O y) : order_scope. | Notation | <=^l 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 | |
"<=^l y :> T" | := (<=^l (y : T)) (only parsing) : order_scope. | Notation | <=^l 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 | |
">=^l y" | := (<=^l%O y) : order_scope. | Notation | >=^l 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 | |
">=^l y :> T" | := (>=^l (y : T)) (only parsing) : order_scope. | Notation | >=^l 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 | |
"<^l y" | := (>^l%O y) : order_scope. | Notation | <^l 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 | |
"<^l y :> T" | := (<^l (y : T)) (only parsing) : order_scope. | Notation | <^l 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 | |
">^l y" | := (<^l%O y) : order_scope. | Notation | >^l 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 | |
">^l y :> T" | := (>^l (y : T)) (only parsing) : order_scope. | Notation | >^l 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 <=^l y" | := (<=^l%O x y) : order_scope. | Notation | x <=^l 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 <=^l y :> T" | := ((x : T) <=^l (y : T)) (only parsing) : order_scope. | Notation | x <=^l 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 >=^l y" | := (y <=^l x) (only parsing) : order_scope. | Notation | x >=^l 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 >=^l y :> T" | := ((x : T) >=^l (y : T)) (only parsing) : order_scope. | Notation | x >=^l 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 <^l y" | := (<^l%O x y) : order_scope. | Notation | x <^l 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 <^l y :> T" | := ((x : T) <^l (y : T)) (only parsing) : order_scope. | Notation | x <^l 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 >^l y" | := (y <^l x) (only parsing) : order_scope. | Notation | x >^l 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 >^l y :> T" | := ((x : T) >^l (y : T)) (only parsing) : order_scope. | Notation | x >^l 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 <=^l y <=^l z" | := ((x <=^l y) && (y <=^l z)) : order_scope. | Notation | x <=^l y <=^l 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 <^l y <=^l z" | := ((x <^l y) && (y <=^l z)) : order_scope. | Notation | x <^l y <=^l 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 <=^l y <^l z" | := ((x <=^l y) && (y <^l z)) : order_scope. | Notation | x <=^l y <^l 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 <^l y <^l z" | := ((x <^l y) && (y <^l z)) : order_scope. | Notation | x <^l y <^l 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 <=^l y ?= 'iff' C" | := (<?=^l%O x y C) : order_scope. | Notation | x <=^l 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 <=^l y ?= 'iff' C :> T" | := ((x : T) <=^l (y : T) ?= iff C)
(only parsing) : order_scope. | Notation | x <=^l 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 | |
">=<^l y" | := [pred x | >=<^l%O x y] : order_scope. | Notation | >=<^l 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 | |
">=<^l y :> T" | := (>=<^l (y : T)) (only parsing) : order_scope. | Notation | >=<^l 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 >=<^l y" | := (>=<^l%O x y) : order_scope. | Notation | x >=<^l 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 | |
"><^l y" | := [pred x | ~~ (>=<^l%O x y)] : order_scope. | Notation | ><^l 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 | |
"><^l y :> T" | := (><^l (y : T)) (only parsing) : order_scope. | Notation | ><^l 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 ><^l y" | := (~~ (><^l%O x y)) : order_scope. | Notation | x ><^l 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 | |
"<=^l%O" | := (@le (seqlexi_display _ _) _) : function_scope. | Notation | <=^l%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",
"seqlexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=^l%O" | := (@ge (seqlexi_display _ _) _) : function_scope. | Notation | >=^l%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",
"seqlexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<^l%O" | := (@lt (seqlexi_display _ _) _) : function_scope. | Notation | <^l%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",
"seqlexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">^l%O" | := (@gt (seqlexi_display _ _) _) : function_scope. | Notation | >^l%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",
"seqlexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<?=^l%O" | := (@leif (seqlexi_display _ _) _) : function_scope. | Notation | <?=^l%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",
"seqlexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
">=<^l%O" | := (@comparable (seqlexi_display _ _) _) : function_scope. | Notation | >=<^l%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",
"seqlexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"><^l%O" | := (fun x y => ~~ (@comparable (seqlexi_display _ _) _ x y)) :
function_scope. | Notation | ><^l%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",
"seqlexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
type (disp : disp_t) (T T' : Type) | := T * T'. | Definition | type | 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... | [
"T'",
"disp_t"
] | FIXME | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
type_
(disp1 disp2 : disp_t) (T : preorderType disp1) (T' : preorderType disp2) | :=
type (prod_display disp1 disp2) T T'. | Definition | type_ | 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... | [
"T'",
"disp_t",
"prod_display",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"T * T'" | := (type disp T T') : type_scope. | Notation | T * 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... | [
"T'",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
le x y | := (x.1 <= y.1) && (x.2 <= y.2). | Let | le | 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 | |
lt x y | := (x.1 < y.1) && (x.2 <= y.2) || (x.1 <= y.1) && (x.2 < y.2). | Let | 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... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lt_def x y : lt x y = le x y && ~~ le y x. | Proof.
rewrite /lt /le !lt_leAnge -andbA -andb_orr.
by rewrite [~~ _ && _]andbC -andb_orr andbA negb_and.
Qed. | Fact | lt_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... | [
"le",
"lt",
"lt_leAnge"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
refl : reflexive le. | Proof. by move=> ?; rewrite /le !lexx. Qed. | Fact | refl | 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",
"lexx"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
trans : transitive le. | Proof.
rewrite /le => y x z /andP [] hxy ? /andP [] /(le_trans hxy) ->.
by apply: le_trans.
Qed. | Fact | trans | 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",
"le",
"le_trans"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
leEprod x y : (x <= y) = (x.1 <= y.1) && (x.2 <= y.2). | Proof. by []. Qed. | Lemma | leEprod | 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 | |
ltEprod x y :
(x < y) = (x.1 < y.1) && (x.2 <= y.2) || (x.1 <= y.1) && (x.2 < y.2). | Proof.
rewrite lt_leAnge !leEprod negb_and andb_orr andbAC -lt_leAnge -andbA.
by rewrite -lt_leAnge.
Qed. | Lemma | ltEprod | 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... | [
"leEprod",
"lt_leAnge"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
le_pair (x1 y1 : T1) (x2 y2 : T2) :
((x1, x2) <= (y1, y2) :> T1 * T2) = (x1 <= y1) && (x2 <= y2). | Proof. by []. Qed. | Lemma | le_pair | 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 | |
lt_pair (x1 y1 : T1) (x2 y2 : T2) :
((x1, x2) < (y1, y2) :> T1 * T2)
= (x1 < y1) && (x2 <= y2) || (x1 <= y1) && (x2 < y2). | Proof. exact/ltEprod. Qed. | Lemma | lt_pair | 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... | [
"ltEprod"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
le0x x : (\bot, \bot) <= x :> T1 * T2. | Proof. by rewrite leEprod !le0x. Qed. | Fact | le0x | 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",
"leEprod"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
botEprod : \bot = (\bot, \bot) :> T1 * T2. | Proof. by []. Qed. | Lemma | botEprod | 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"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
topEprod : \top = (\top, \top) :> T1 * T2. | Proof. by []. Qed. | Lemma | topEprod | 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... | [
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"T *prod[ d ] T'" | := (type d T T')
(at level 70, d at next level, format "T *prod[ d ] T'") : type_scope. | Notation | T *prod[ d ] 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... | [
"T'",
"next",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"T *p T'" | := (type_ T T')
(at level 70, format "T *p T'") : type_scope. | Notation | T *p 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... | [
"T'",
"type_"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
leEprod | := @leEprod. | Definition | leEprod | 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 | |
le_pair | := @le_pair. | Definition | le_pair | 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 | |
botEprod | := @botEprod. | Definition | botEprod | 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 | |
topEprod | := @topEprod. | Definition | topEprod | 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 | |
type_
(disp1 disp2 : disp_t) (T : preorderType disp1) (T' : preorderType disp2) | :=
type (lexi_display disp1 disp2) T T'. | Definition | type_ | 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... | [
"T'",
"disp_t",
"lexi_display",
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
le x y | := (x.1 <= y.1) && ((x.1 >= y.1) ==> (x.2 <= y.2)). | Let | le | 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 |
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