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 |
|---|---|---|---|---|---|---|---|---|---|---|
"\bot" | := (@bottom (lexi_display _ _) _). | Notation | \bot | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"lexi_display"
] | notations later. Do not remove them. | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
"\top" | := (@top (lexi_display _ _) _). | Notation | \top | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"lexi_display",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
meet | := (@meet (lexi_display _ _) _). | Notation | meet | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
join | := (@join (lexi_display _ _) _). | Notation | join | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
min | := (@min (lexi_display _ _) _). | Notation | min | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
max | := (@max (lexi_display _ _) _). | Notation | max | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"lexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( i <- r | P ) F" | :=
(\big[join / \bot]_(i <- r | P%B) F%O) : order_scope. | Notation | \join^l_ ( i <- r | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( i <- r ) F" | :=
(\big[join / \bot]_(i <- r) F%O) : order_scope. | Notation | \join^l_ ( i <- r ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( i | P ) F" | :=
(\big[join / \bot]_(i | P%B) F%O) : order_scope. | Notation | \join^l_ ( i | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ i F" | :=
(\big[join / \bot]_i F%O) : order_scope. | Notation | \join^l_ i F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( i : I | P ) F" | :=
(\big[join / \bot]_(i : I | P%B) F%O) (only parsing) : order_scope. | Notation | \join^l_ ( i : I | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( i : I ) F" | :=
(\big[join / \bot]_(i : I) F%O) (only parsing) : order_scope. | Notation | \join^l_ ( i : I ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( m <= i < n | P ) F" | :=
(\big[join / \bot]_(m <= i < n | P%B) F%O) : order_scope. | Notation | \join^l_ ( m <= i < n | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( m <= i < n ) F" | :=
(\big[join / \bot]_(m <= i < n) F%O) : order_scope. | Notation | \join^l_ ( m <= i < n ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( i < n | P ) F" | :=
(\big[join / \bot]_(i < n | P%B) F%O) : order_scope. | Notation | \join^l_ ( i < n | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( i < n ) F" | :=
(\big[join / \bot]_(i < n) F%O) : order_scope. | Notation | \join^l_ ( i < n ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( i 'in' A | P ) F" | :=
(\big[join / \bot]_(i in A | P%B) F%O) : order_scope. | Notation | \join^l_ ( i 'in' A | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\join^l_ ( i 'in' A ) F" | :=
(\big[join / \bot]_(i in A) F%O) : order_scope. | Notation | \join^l_ ( i 'in' A ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"join"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( i <- r | P ) F" | :=
(\big[meet / \top]_(i <- r | P%B) F%O) : order_scope. | Notation | \meet^l_ ( i <- r | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( i <- r ) F" | :=
(\big[meet / \top]_(i <- r) F%O) : order_scope. | Notation | \meet^l_ ( i <- r ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( i | P ) F" | :=
(\big[meet / \top]_(i | P%B) F%O) : order_scope. | Notation | \meet^l_ ( i | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ i F" | :=
(\big[meet / \top]_i F%O) : order_scope. | Notation | \meet^l_ i F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( i : I | P ) F" | :=
(\big[meet / \top]_(i : I | P%B) F%O) (only parsing) : order_scope. | Notation | \meet^l_ ( i : I | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( i : I ) F" | :=
(\big[meet / \top]_(i : I) F%O) (only parsing) : order_scope. | Notation | \meet^l_ ( i : I ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( m <= i < n | P ) F" | :=
(\big[meet / \top]_(m <= i < n | P%B) F%O) : order_scope. | Notation | \meet^l_ ( m <= i < n | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( m <= i < n ) F" | :=
(\big[meet / \top]_(m <= i < n) F%O) : order_scope. | Notation | \meet^l_ ( m <= i < n ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( i < n | P ) F" | :=
(\big[meet / \top]_(i < n | P%B) F%O) : order_scope. | Notation | \meet^l_ ( i < n | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( i < n ) F" | :=
(\big[meet / \top]_(i < n) F%O) : order_scope. | Notation | \meet^l_ ( i < n ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( i 'in' A | P ) F" | :=
(\big[meet / \top]_(i in A | P%B) F%O) : order_scope. | Notation | \meet^l_ ( i 'in' A | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\meet^l_ ( i 'in' A ) F" | :=
(\big[meet / \top]_(i in A) F%O) : order_scope. | Notation | \meet^l_ ( i 'in' A ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ i F" | :=
(\big[min/top]_i F) : order_scope. | Notation | \min^l_ i F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( i <- r | P ) F" | :=
(\big[min/top]_(i <- r | P%B) F%O) : order_scope. | Notation | \min^l_ ( i <- r | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( i < r ) F" | :=
(\big[min/top]_(i <- r) F%O) : order_scope. | Notation | \min^l_ ( i < r ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( m <= i < n | P ) F" | :=
(\big[min/top]_(m <= i < n | P%B) F%O) : order_scope. | Notation | \min^l_ ( m <= i < n | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( m <= i < n ) F" | :=
(\big[min/top]_(m <= i < n) F%O) : order_scope. | Notation | \min^l_ ( m <= i < n ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( i | P ) F" | :=
(\big[min/top]_(i | P%B) F%O) : order_scope. | Notation | \min^l_ ( i | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( i : t | P ) F" | :=
(\big[min/top]_(i : t | P%B) F%O) (only parsing) : order_scope. | Notation | \min^l_ ( i : t | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( i : t ) F" | :=
(\big[min/top]_(i : t) F%O) (only parsing) : order_scope. | Notation | \min^l_ ( i : t ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( i < n | P ) F" | :=
(\big[min/top]_(i < n | P%B) F%O) : order_scope. | Notation | \min^l_ ( i < n | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( i < n ) F" | :=
(\big[min/top]_(i < n) F%O) : order_scope. | Notation | \min^l_ ( i < n ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( i 'in' A | P ) F" | :=
(\big[min/top]_(i in A | P%B) F%O) : order_scope. | Notation | \min^l_ ( i 'in' A | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\min^l_ ( i 'in' A ) F" | :=
(\big[min/top]_(i in A) F%O) : order_scope. | Notation | \min^l_ ( i 'in' A ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"min",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ i F" | :=
(\big[max/bottom]_i F%O) : order_scope. | Notation | \max^l_ i F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( i <- r | P ) F" | :=
(\big[max/bottom]_(i <- r | P%B) F%O) : order_scope. | Notation | \max^l_ ( i <- r | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( i < r ) F" | :=
(\big[max/bottom]_(i <- r) F%O) : order_scope. | Notation | \max^l_ ( i < r ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( m <= i < n | P ) F" | :=
(\big[max/bottom]_(m <= i < n | P%B) F%O) : order_scope. | Notation | \max^l_ ( m <= i < n | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( m <= i < n ) F" | :=
(\big[max/bottom]_(m <= i < n) F%O) : order_scope. | Notation | \max^l_ ( m <= i < n ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( i | P ) F" | :=
(\big[max/bottom]_(i | P%B) F%O) : order_scope. | Notation | \max^l_ ( i | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( i : t | P ) F" | :=
(\big[max/bottom]_(i : t | P%B) F%O) (only parsing) : order_scope. | Notation | \max^l_ ( i : t | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( i : t ) F" | :=
(\big[max/bottom]_(i : t) F%O) (only parsing) : order_scope. | Notation | \max^l_ ( i : t ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( i < n | P ) F" | :=
(\big[max/bottom]_(i < n | P%B) F%O) : order_scope. | Notation | \max^l_ ( i < n | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( i < n ) F" | :=
(\big[max/bottom]_(i < n) F%O) : order_scope. | Notation | \max^l_ ( i < n ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( i 'in' A | P ) F" | :=
(\big[max/bottom]_(i in A | P%B) F%O) : order_scope. | Notation | \max^l_ ( i 'in' A | P ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"\max^l_ ( i 'in' A ) F" | :=
(\big[max/bottom]_(i in A) F%O) : order_scope. | Notation | \max^l_ ( i 'in' A ) F | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bottom",
"max"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
meetlexi | := (@meet (seqlexi_display _) _). | Notation | meetlexi | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"meet",
"seqlexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
joinlexi | := (@join (seqlexi_display _) _). | Notation | joinlexi | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"join",
"seqlexi_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
anti : antisymmetric (@le disp1 disp2 disp2 T1 T2). | Proof.
case=> [? ?] [? ?].
by rewrite andbAC andbA andbAC -andbA => /= /andP [] /le_anti -> /le_anti ->.
Qed. | Fact | anti | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"le",
"le_anti"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"T1 * T2" | := (type disp3 T1 T2) : type_scope. | Notation | T1 * T2 | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
T1' : Type | := T1. | Let | T1' | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
T2' : Type | := T2. | Let | T2' | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltEprod x y : (x < y) = [&& x != y, x.1 <= y.1 & x.2 <= y.2]. | Proof. by rewrite lt_neqAle. Qed. | Lemma | ltEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"lt_neqAle"
] | 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. by rewrite ltEprod negb_and. Qed. | Lemma | lt_pair | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"ltEprod"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"T1 * T2" | := (type (Disp tt tt) T1 T2) : type_scope. | Notation | T1 * T2 | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"type"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
meet x y | := (x.1 `&` y.1, x.2 `&` y.2). | Let | meet | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lexI x y z : (x <= meet y z) = (x <= y) && (x <= z). | Proof. by rewrite leEprod !lexI andbACA. Qed. | Fact | lexI | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"leEprod",
"meet"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
meetEprod x y : x `&` y = (x.1 `&` y.1, x.2 `&` y.2). | Proof. by []. Qed. | Lemma | meetEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
join x y | := (x.1 `|` y.1, x.2 `|` y.2). | Definition | join | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
joinEprod x y : x `|` y = (x.1 `|` y.1, x.2 `|` y.2). | Proof. by []. Qed. | Lemma | joinEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
meetUl : @left_distributive (T1 * T2) _ Order.meet Order.join. | Proof. by move=> ? ? ?; rewrite meetEprod !meetUl. Qed. | Fact | meetUl | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"join",
"meet",
"meetEprod"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rcompl x y z | := (rcompl x.1 y.1 z.1, rcompl x.2 y.2 z.2). | Let | rcompl | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rcomplPmeet x y z : ((x `&` y) `|` z) `&` rcompl x y z = x `&` y. | Proof. by rewrite !(meetEprod, joinEprod) !rcomplPmeet. Qed. | Fact | rcomplPmeet | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"joinEprod",
"meetEprod",
"rcompl"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rcomplEprod x y z :
rcompl x y z = (Order.rcompl x.1 y.1 z.1, Order.rcompl x.2 y.2 z.2). | Proof. by []. Qed. | Lemma | rcomplEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"rcompl"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
diff x y | := (diff x.1 y.1, diff x.2 y.2). | Let | diff | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
diffErcompl x y : diff x y = rcompl \bot x y. | Proof. by rewrite /diff !diffErcompl. Qed. | Fact | diffErcompl | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"bot",
"diff",
"rcompl"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
diffEprod x y : x `\` y = (x.1 `\` y.1, x.2 `\` y.2). | Proof. by []. Qed. | Lemma | diffEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
codiff x y | := (codiff x.1 y.1, codiff x.2 y.2). | Definition | codiff | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
codiffEprod x y :
codiff x y = (Order.codiff x.1 y.1, Order.codiff x.2 y.2). | Proof. by []. Qed. | Lemma | codiffEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"codiff"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
compl x | := (~` x.1, ~` x.2). | Let | compl | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
complEdiff x : compl x = (\top : T1 * T2) `\` x. | Proof. by rewrite /compl !complEdiff. Qed. | Fact | complEdiff | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"compl",
"top"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
complEprod x : ~` x = (~` x.1, ~` x.2). | Proof. by []. Qed. | Lemma | complEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltEprod | := @ltEprod. | Definition | ltEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lt_pair | := @lt_pair. | Definition | lt_pair | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
meetEprod | := @meetEprod. | Definition | meetEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
joinEprod | := @joinEprod. | Definition | joinEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
rcomplEprod | := @rcomplEprod. | Definition | rcomplEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
diffEprod | := @diffEprod. | Definition | diffEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
codiffEprod | := @codiffEprod. | Definition | codiffEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
complEprod | := @complEprod. | Definition | complEprod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
prod T1 T2 | := T1 *prod[prod_display disp1 disp2] T2. | Let | prod | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"prod_display"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
le x y | := (tag x <= tag y) &&
((tag x >= tag y) ==> (tagged x <= tagged_as x y)). | Definition | le | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"tagged_as"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lt x y | := (tag x <= tag y) &&
((tag x >= tag y) ==> (tagged x < tagged_as x y)). | Definition | lt | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"tagged_as"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
refl : reflexive le. | Proof. by move=> [x x']; rewrite /le tagged_asE/= !lexx. Qed. | Fact | refl | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"le",
"lexx",
"tagged_asE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
anti : antisymmetric le. | Proof.
rewrite /le => -[x x'] [y y']/=; case: comparableP => //= eq_xy.
by case: _ / eq_xy in y' *; rewrite !tagged_asE => /le_anti ->.
Qed. | Fact | anti | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"comparableP",
"le",
"le_anti",
"tagged_asE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
trans : transitive le. | Proof.
move=> [y y'] [x x'] [z z'] /andP[/= lexy lexy'] /andP[/= leyz leyz'].
rewrite /= /le (le_trans lexy) //=; apply/implyP => lezx.
elim: _ / (@le_anti _ _ x y) in y' z' lexy' leyz' *; last first.
by rewrite lexy (le_trans leyz).
elim: _ / (@le_anti _ _ x z) in z' leyz' *; last by rewrite (le_trans lexy).
by rewr... | Fact | trans | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"apply",
"last",
"le",
"le_anti",
"le_trans",
"lexx",
"tagged_asE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lt_le_def x y : lt x y = le x y && ~~ le y x. | Proof.
rewrite /lt /le; case: x y => [x x'] [y y']//=.
case: (comparableP x y) => //= xy.
by subst y; rewrite !tagged_asE lt_le_def.
Qed. | Fact | lt_le_def | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"comparableP",
"le",
"lt",
"tagged_asE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
leEsig x y : (x <= y) =
(tag x <= tag y) && ((tag x >= tag y) ==> (tagged x <= tagged_as x y)). | Proof. by []. Qed. | Lemma | leEsig | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"tagged_as"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ltEsig x y : (x < y) =
(tag x <= tag y) && ((tag x >= tag y) ==> (tagged x < tagged_as x y)). | Proof. by []. Qed. | Lemma | ltEsig | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"tagged_as"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
le_Taggedl x (u : T' (tag x)) : (Tagged T' u <= x) = (u <= tagged x). | Proof. by case: x => [t v]/= in u *; rewrite leEsig/= lexx/= tagged_asE. Qed. | Lemma | le_Taggedl | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"T'",
"leEsig",
"lexx",
"tagged_asE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
le_Taggedr x (u : T' (tag x)) : (x <= Tagged T' u) = (tagged x <= u). | Proof. by case: x => [t v]/= in u *; rewrite leEsig/= lexx/= tagged_asE. Qed. | Lemma | le_Taggedr | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"T'",
"leEsig",
"lexx",
"tagged_asE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
lt_Taggedl x (u : T' (tag x)) : (Tagged T' u < x) = (u < tagged x). | Proof. by case: x => [t v]/= in u *; rewrite ltEsig/= lexx/= tagged_asE. Qed. | Lemma | lt_Taggedl | order | order/order.v | [
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"choice",
"seq",
"path",
"fintype",
"tuple",
"bigop",
"finset",
"div",
"prime",
"finfun",
"preorder",
"Order",
"BPreorderTheory",
"PreCancelPartial",
"OrderMorphismTheory",
"NatOrder",... | [
"T'",
"lexx",
"ltEsig",
"tagged_asE"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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