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 |
|---|---|---|---|---|---|---|---|---|---|---|
of_uint (d:Decimal.uint) : N | :=
match d with
| Decimal.Nil => N0
| Decimal.D0 l => of_uint l
| Decimal.D1 l => Npos (of_uint_acc l 1)
| Decimal.D2 l => Npos (of_uint_acc l 1~0)
| Decimal.D3 l => Npos (of_uint_acc l 1~1)
| Decimal.D4 l => Npos (of_uint_acc l 1~0~0)
| Decimal.D5 l => Npos (of_uint_acc l 1~0~1)
| Decimal.D6 l => Npo... | Fixpoint | of_uint | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Nil",
"of_uint_acc"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sixteen | := (xO (xO (xO (xO xH)))). | Notation | sixteen | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
of_hex_uint_acc (d:Hexadecimal.uint) (acc:positive) | :=
match d with
| Hexadecimal.Nil => acc
| Hexadecimal.D0 l => of_hex_uint_acc l (mul sixteen acc)
| Hexadecimal.D1 l => of_hex_uint_acc l (add 1 (mul sixteen acc))
| Hexadecimal.D2 l => of_hex_uint_acc l (add 1~0 (mul sixteen acc))
| Hexadecimal.D3 l => of_hex_uint_acc l (add 1~1 (mul sixteen acc))
| Hex... | Fixpoint | of_hex_uint_acc | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Da",
"Nil",
"add",
"mul",
"sixteen"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
of_hex_uint (d:Hexadecimal.uint) : N | :=
match d with
| Hexadecimal.Nil => N0
| Hexadecimal.D0 l => of_hex_uint l
| Hexadecimal.D1 l => Npos (of_hex_uint_acc l 1)
| Hexadecimal.D2 l => Npos (of_hex_uint_acc l 1~0)
| Hexadecimal.D3 l => Npos (of_hex_uint_acc l 1~1)
| Hexadecimal.D4 l => Npos (of_hex_uint_acc l 1~0~0)
| Hexadecimal.D5 l => Np... | Fixpoint | of_hex_uint | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Da",
"Nil",
"of_hex_uint_acc"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
of_int (d:Decimal.int) : option positive | :=
match d with
| Decimal.Pos d =>
match of_uint d with
| N0 => None
| Npos p => Some p
end
| Decimal.Neg _ => None
end. | Definition | of_int | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"int",
"of_uint"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
of_hex_int (d:Hexadecimal.int) : option positive | :=
match d with
| Hexadecimal.Pos d =>
match of_hex_uint d with
| N0 => None
| Npos p => Some p
end
| Hexadecimal.Neg _ => None
end. | Definition | of_hex_int | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"int",
"of_hex_uint"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
of_num_int (d:Number.int) : option positive | :=
match d with
| Number.IntDecimal d => of_int d
| Number.IntHexadecimal d => of_hex_int d
end. | Definition | of_num_int | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"int",
"of_hex_int",
"of_int"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
to_little_uint p | :=
match p with
| xH => Decimal.D1 Decimal.Nil
| xI p => Decimal.Little.succ_double (to_little_uint p)
| xO p => Decimal.Little.double (to_little_uint p)
end. | Fixpoint | to_little_uint | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Nil",
"double"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
to_uint p | := Decimal.rev (to_little_uint p). | Definition | to_uint | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"rev",
"to_little_uint"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
to_num_uint p | := Number.UIntDecimal (to_uint p). | Definition | to_num_uint | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"to_uint"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Nsucc n | :=
match n with
| N0 => Npos xH
| Npos p => Npos (Pos.succ p)
end. | Definition | Nsucc | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [] | ** Successor | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
nat_of_succ_bin b : nat_of_bin (Nsucc b) = 1 + nat_of_bin b :> nat. | Proof. by case: b => [//|p /=]; rewrite nat_of_succ_pos. Qed. | Lemma | nat_of_succ_bin | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Nsucc",
"nat",
"nat_of_bin",
"nat_of_succ_pos"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eqb_eq p q : Pos.eqb p q = true <-> p=q. | Proof.
by elim: p q => [p IHp|p IHp|] [q|q|] //=; split=> [/IHp->//|]; case=> /IHp.
Qed. | Theorem | eqb_eq | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"eqb",
"split"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
syntax | := Leaf of positive | Op of syntax & syntax. | Inductive | syntax | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Leaf"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
serial | := (fix loop (acc : seq positive) (s : syntax) :=
match s with
| Leaf n => n :: acc
| Op s s' => (loop^~ s (loop^~ s' acc))
end) [::]. | Coercion | serial | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Leaf",
"seq",
"syntax"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
serial_Op s1 s2 : Op s1 s2 = s1 ++ s2 :> seq _. | Proof.
rewrite /serial; set loop := (X in X [::]); rewrite -/loop.
elim: s1 (loop [::] s2) => [n|s11 IHs1 s12 IHs2] //= l.
by rewrite IHs1 [in RHS]IHs1 IHs2 catA.
Qed. | Lemma | serial_Op | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"catA",
"s1",
"s12",
"s2",
"seq",
"serial"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Leaf_of_nat n | := Leaf (Pos.sub (pos_of_nat n n) xH). | Definition | Leaf_of_nat | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Leaf",
"pos_of_nat",
"sub"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Leaf : positive >-> syntax. | Coercion | Leaf | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"syntax"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | ||
Leaf_of_nat : nat >-> syntax. | Coercion | Leaf_of_nat | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"nat",
"syntax"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | ||
"x * y" | := (Op x%AC y%AC) : AC_scope. | Notation | x * y | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pattern (s : syntax) | := ((fix loop n s :=
match s with
| Leaf 1%positive => (Leaf n, Pos.succ n)
| Leaf m => Pos.iter (fun oi => (Op oi.1 (Leaf oi.2), Pos.succ oi.2))
(Leaf n, Pos.succ n) (Pos.sub m xH)
| Op s s' => let: (p, n') := loop n s in
let: (p', n'') := loop n' s' in
(Op ... | Definition | pattern | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Leaf",
"iter",
"n'",
"sub",
"syntax"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
env | := Empty | ENode of T & env & env. | Inductive | env | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pos | := fix loop (e : env) p {struct e} :=
match e, p with
| ENode t _ _, 1%positive => t
| ENode t e _, (p~0)%positive => loop e p
| ENode t _ e, (p~1)%positive => loop e p
| _, _ => idx
end. | Definition | pos | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"env"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
set_pos (f : T -> T) | := fix loop e p {struct p} :=
match e, p with
| ENode t e e', 1%positive => ENode (f t) e e'
| ENode t e e', (p~0)%positive => ENode t (loop e p) e'
| ENode t e e', (p~1)%positive => ENode t e (loop e' p)
| Empty, 1%positive => ENode (f idx) Empty Empty
| Empty, (p~0)%positive => ENode idx (loop Empty p) Empty
... | Definition | set_pos | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"e'"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
pos_set_pos (f : T -> T) e (p p' : positive) :
pos (set_pos f e p) p' = if p == p' then f (pos e p) else pos e p'. | Proof. by elim: p e p' => [p IHp|p IHp|] [|???] [?|?|]//=; rewrite IHp. Qed. | Lemma | pos_set_pos | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"pos",
"set_pos"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
unzip z (e : env) : env | := match z with
| [::] => e
| (x, inl e') :: z' => unzip z' (ENode x e' e)
| (x, inr e') :: z' => unzip z' (ENode x e e')
end. | Fixpoint | unzip | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"e'",
"env"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
set_pos_trec (f : T -> T) | := fix loop z e p {struct p} :=
match e, p with
| ENode t e e', 1%positive => unzip z (ENode (f t) e e')
| ENode t e e', (p~0)%positive => loop ((t, inr e') :: z) e p
| ENode t e e', (p~1)%positive => loop ((t, inl e) :: z) e' p
| Empty, 1%positive => unzip z (ENode (f idx) Empty Empty)
| Empty, (p~0)%positive =... | Definition | set_pos_trec | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"e'",
"unzip"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
set_pos_trecE f z e p : set_pos_trec f z e p = unzip z (set_pos f e p). | Proof. by elim: p e z => [p IHp|p IHp|] [|???] [|[??]?] //=; rewrite ?IHp. Qed. | Lemma | set_pos_trecE | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"set_pos",
"set_pos_trec",
"unzip"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eval (e : env) | := fix loop (s : syntax) :=
match s with
| Leaf n => pos e n
| Op s s' => op (loop s) (loop s')
end. | Definition | eval | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Leaf",
"env",
"pos",
"syntax"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
content | := (fix loop (acc : env N) s :=
match s with
| Leaf n => set_pos_trec N0 Pos.Nsucc [::] acc n
| Op s s' => loop (loop acc s') s
end) Empty. | Definition | content | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Leaf",
"Nsucc",
"env",
"set_pos_trec"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
count_memE x (t : syntax) :
count_mem x t = nat_of_bin (pos N0 (content t) x). | Proof.
rewrite /content; set loop := (X in X Empty); rewrite -/loop.
rewrite -[LHS]addn0.
have <- : nat_of_bin (pos N0 Empty x) = 0 :> nat by elim: x.
elim: t Empty => [n|s IHs s' IHs'] e //=; last first.
by rewrite serial_Op count_cat -addnA IHs' IHs.
rewrite ?addn0 set_pos_trecE pos_set_pos; case: (altP eqP) => [->... | Lemma | count_memE | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"addn0",
"addnA",
"content",
"count_cat",
"count_mem",
"last",
"nat",
"nat_of_bin",
"nat_of_succ_bin",
"pos",
"pos_set_pos",
"serial_Op",
"set_pos_trecE",
"syntax"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
cforall N T : env N -> (env T -> Type) -> Type | := env_rect (@^~ Empty)
(fun _ e IHe e' IHe' R => forall x, IHe (fun xe => IHe' (R \o ENode x xe))). | Definition | cforall | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"e'",
"env"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
cforallP N T R : (forall e : env T, R e) -> forall (e : env N), cforall e R. | Proof.
move=> Re e; elim: e R Re => [|? e /= IHe e' IHe' ?? x] //=.
by apply: IHe => ?; apply: IHe' => /=.
Qed. | Lemma | cforallP | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"Re",
"apply",
"cforall",
"e'",
"env"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
proof (p s : syntax) : content p = content s ->
forall env, eval idx op env p = eval idx op env s. | Proof.
suff evalE env t : eval idx op env t = \big[op/idx]_(i <- t) (pos idx env i).
move=> cps e; rewrite !evalE; apply: perm_big.
by apply/allP => x _ /=; rewrite !count_memE cps.
elim: t => //= [n|t -> t' ->]; last by rewrite serial_Op big_cat.
by rewrite big_cons big_nil Monoid.mulm1.
Qed. | Lemma | proof | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"allP",
"apply",
"big_cat",
"big_cons",
"big_nil",
"content",
"count_memE",
"cps",
"env",
"eval",
"last",
"mulm1",
"perm_big",
"pos",
"serial_Op",
"syntax"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
direct p s ps | := cforallP (@proof p s ps) (content p). | Definition | direct | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"cforallP",
"content",
"proof"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
AC_check_pattern | :=
(ltac: (match goal with
|- AC.content ?pat = AC.content ?ord =>
let pat' := fresh "pat" in let pat' := eval compute in pat in
tryif unify pat' ord then
fail 1 "AC: equality between" pat
"and" ord "is trivial, cannot progress"
else tryif vm_compute; reflexivity the... | Notation | AC_check_pattern | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC",
"content",
"eval",
"unify"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
opACof law p s | :=
((fun T idx op assoc lid rid comm => (change_type (@AC.direct T idx
(Monoid.ComLaw.Pack (* FIXME: find a way to make this robust to hierarchy evolutions *)
(Monoid.ComLaw.Class
(SemiGroup.isLaw.Axioms_ op assoc)
(Monoid.isMonoidLaw.Axioms_ idx op lid rid)
(SemiGroup.isCommutative... | Notation | opACof | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC",
"AC_check_pattern",
"cbvrefl",
"change_type",
"comm",
"direct",
"law",
"mul1m",
"mulm1",
"mulmA",
"mulmC"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
opAC op p s | := (opACof op (AC.pattern p%AC) s%AC) (only parsing). | Notation | opAC | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC",
"opACof",
"pattern"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
opACl op s | := (opAC op (AC.Leaf_of_nat (size (AC.serial s%AC))) s%AC)
(only parsing). | Notation | opACl | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC",
"Leaf_of_nat",
"opAC",
"serial",
"size"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"op .[ 'ACof' p s ]" | := (opACof op p%AC s%AC) (only parsing). | Notation | op .[ 'ACof' p s ] | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC",
"opACof"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"op .[ 'AC' p s ]" | := (opAC op p%AC s%AC) (only parsing). | Notation | op .[ 'AC' p s ] | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC",
"opAC"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"op .[ 'ACl' s ]" | := (opACl op s%AC) (only parsing). | Notation | op .[ 'ACl' s ] | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC",
"opACl"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
AC_strategy | :=
(ltac: (cbv -[Monoid.ComLaw.sort Monoid.Law.sort]; reflexivity))
(only parsing). | Notation | AC_strategy | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"sort"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ACof p s | := (change_type
(@AC.direct _ _ _ p%AC s%AC AC_check_pattern) AC_strategy)
(only parsing). | Notation | ACof | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC",
"AC_check_pattern",
"AC_strategy",
"change_type",
"direct"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
AC p s | := (ACof (AC.pattern p%AC) s%AC) (only parsing). | Notation | AC | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"ACof",
"pattern"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ACl s | := (AC (AC.Leaf_of_nat (size (AC.serial s%AC))) s%AC)
(only parsing). | Notation | ACl | boot | boot/ssrAC.v | [
"HB",
"structures",
"Corelib",
"PosDef",
"mathcomp",
"ssreflect",
"ssrbool",
"ssrfun",
"ssrnat",
"eqtype",
"seq",
"bigop",
"Pos",
"AC.Syntax",
"AC.Exports"
] | [
"AC",
"Leaf_of_nat",
"serial",
"size"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
homo_mono1 [aT rT : Type] [f : aT -> rT] [g : rT -> aT]
[aP : pred aT] [rP : pred rT] :
cancel g f ->
{homo f : x / aP x >-> rP x} ->
{homo g : x / rP x >-> aP x} -> {mono g : x / rP x >-> aP x}. | Proof. by move=> gK fP gP x; apply/idP/idP => [/fP|/gP//]; rewrite gK. Qed. | Lemma | homo_mono1 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"aP",
"aT",
"apply",
"fP",
"gK"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
if_and b1 b2 T (x y : T) :
(if b1 && b2 then x else y) = (if b1 then if b2 then x else y else y). | Proof. by case: b1 b2 => [] []. Qed. | Lemma | if_and | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
if_or b1 b2 T (x y : T) :
(if b1 || b2 then x else y) = (if b1 then x else if b2 then x else y). | Proof. by case: b1 b2 => [] []. Qed. | Lemma | if_or | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
if_implyb b1 b2 T (x y : T) :
(if b1 ==> b2 then x else y) = (if b1 then if b2 then x else y else x). | Proof. by case: b1 b2 => [] []. Qed. | Lemma | if_implyb | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
if_implybC b1 b2 T (x y : T) :
(if b1 ==> b2 then x else y) = (if b2 then x else if b1 then y else x). | Proof. by case: b1 b2 => [] []. Qed. | Lemma | if_implybC | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
if_add b1 b2 T (x y : T) :
(if b1 (+) b2 then x else y) = (if b1 then if b2 then y else x else if b2 then x else y). | Proof. by case: b1 b2 => [] []. Qed. | Lemma | if_add | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
relpre_trans {T' T : Type} {leT : rel T} {f : T' -> T} :
transitive leT -> transitive (relpre f leT). | Proof. by move=> + y x z; apply. Qed. | Lemma | relpre_trans | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"T'",
"apply",
"rel"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and3proj1 (P1 P2 P3 : Prop) (a : [/\ P1, P2 & P3]) | :=
let: And3 p1 p2 p3 := a in p1. | Definition | and3proj1 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | TODO: when backporting to Rocq, change the inductives `and3`, `and4`, `and5`
to records | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
and3proj2 (P1 P2 P3 : Prop) (a : [/\ P1, P2 & P3]) | :=
let: And3 p1 p2 p3 := a in p2. | Definition | and3proj2 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and3proj3 (P1 P2 P3 : Prop) (a : [/\ P1, P2 & P3]) | :=
let: And3 p1 p2 p3 := a in p3. | Definition | and3proj3 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and4proj1 (P1 P2 P3 P4 : Prop) (a : [/\ P1, P2, P3 & P4]) | :=
let: And4 p1 p2 p3 p4 := a in p1. | Definition | and4proj1 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and4proj2 (P1 P2 P3 P4 : Prop) (a : [/\ P1, P2, P3 & P4]) | :=
let: And4 p1 p2 p3 p4 := a in p2. | Definition | and4proj2 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and4proj3 (P1 P2 P3 P4 : Prop) (a : [/\ P1, P2, P3 & P4]) | :=
let: And4 p1 p2 p3 p4 := a in p3. | Definition | and4proj3 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and4proj4 (P1 P2 P3 P4 : Prop) (a : [/\ P1, P2, P3 & P4]) | :=
let: And4 p1 p2 p3 p4 := a in p4. | Definition | and4proj4 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and5proj1 (P1 P2 P3 P4 P5 : Prop) (a : [/\ P1, P2, P3, P4 & P5]) | :=
let: And5 p1 p2 p3 p4 p5 := a in p1. | Definition | and5proj1 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and5proj2 (P1 P2 P3 P4 P5 : Prop) (a : [/\ P1, P2, P3, P4 & P5]) | :=
let: And5 p1 p2 p3 p4 p5 := a in p2. | Definition | and5proj2 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and5proj3 (P1 P2 P3 P4 P5 : Prop) (a : [/\ P1, P2, P3, P4 & P5]) | :=
let: And5 p1 p2 p3 p4 p5 := a in p3. | Definition | and5proj3 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and5proj4 (P1 P2 P3 P4 P5 : Prop) (a : [/\ P1, P2, P3, P4 & P5]) | :=
let: And5 p1 p2 p3 p4 p5 := a in p4. | Definition | and5proj4 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
and5proj5 (P1 P2 P3 P4 P5 : Prop) (a : [/\ P1, P2, P3, P4 & P5]) | :=
let: And5 p1 p2 p3 p4 p5 := a in p5. | Definition | and5proj5 | boot | boot/ssrbool.v | [
"mathcomp",
"ssreflect",
"ssrfun",
"Corelib",
"ssrbool"
] | [
"P1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nosimpl t | := (nosimpl t). | Notation | nosimpl | boot | boot/ssreflect.v | [
"Corelib",
"ssreflect"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
hide {T} t : T | := t. | Definition | hide | boot | boot/ssreflect.v | [
"Corelib",
"ssreflect"
] | [] | Additions to be ported to Corelib ssreflect:
hide t == t, but hide t displays as <hidden>
hideT t == t, but both hideT t and its inferred type display as <hidden>
New ltac views:
=> /#[#hide#]# := insert hide in the type of the top assumption (and
its body if it is a 'let'... | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
hideT | := (@hide (hide _)) (only parsing). | Notation | hideT | boot | boot/ssreflect.v | [
"Corelib",
"ssreflect"
] | [
"hide"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"<hidden >" | := (hide _)
(at level 0, format "<hidden >", only printing) : ssr_scope. | Notation | <hidden > | boot | boot/ssreflect.v | [
"Corelib",
"ssreflect"
] | [
"hide"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"'[' 'hide' ']'" | := (ltac:(
move; lazymatch goal with
| |- forall x : ?A, ?G => change (forall x : hide A, G)
| |- let x : ?A := ?a in ?G => change (let x : hide A := @hide A a in G)
| _ => fail "[hide] : no top assumption"
end)) (at level 0, only parsing) : ssripat_scope. | Notation | '[' 'hide' ']' | boot | boot/ssreflect.v | [
"Corelib",
"ssreflect"
] | [
"hide"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"'[' 'let' ']'" | := (ltac:(
move; lazymatch goal with
| |- forall (H : let x : ?A := ?a in ?T), ?G =>
change (let x : A := a in forall H : T, G)
| |- let H : (let x : ?A := ?a in ?T) := ?t in ?G =>
change (let x : A := a in let H : T := t in G)
| |- let H : ?T := (let x : ?A := ?a in ?t) in ?G =>
change ... | Notation | '[' 'let' ']' | boot | boot/ssreflect.v | [
"Corelib",
"ssreflect"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"'[' 'fix' ']'" | := (ltac:(
match goal with
| |- context [?t] =>
is_fix t; let f := fresh "fix" in set f := t; move: @f => /[hide]
| _ => fail 1 "[fix]: no visible 'fix' in goal"
end)) (at level 0, only parsing) : ssripat_scope. | Notation | '[' 'fix' ']' | boot | boot/ssreflect.v | [
"Corelib",
"ssreflect"
] | [
"hide"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"'[' 'cofix' ']'" | := (ltac:(
match goal with
| |- context [?t] =>
is_cofix t; let z := fresh "cofix" in set z := t; move: @z => /[hide]
| _ => fail 1 "[cofix]: no visible 'cofix' in goal"
end)) (at level 0, only parsing) : ssripat_scope. | Notation | '[' 'cofix' ']' | boot | boot/ssreflect.v | [
"Corelib",
"ssreflect"
] | [
"hide"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
injective2 (rT aT1 aT2 : Type) (f : aT1 -> aT2 -> rT) | :=
forall (x1 x2 : aT1) (y1 y2 : aT2), f x1 y1 = f x2 y2 -> (x1 = x2) * (y1 = y2). | Definition | injective2 | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
inj_omap {aT rT : Type} (f : aT -> rT) :
injective f -> injective (omap f). | Proof. by move=> injf [?|] [?|] //= [/injf->]. Qed. | Lemma | inj_omap | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [
"aT",
"injf"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
omap_id {T : Type} (x : option T) : omap id x = x. | Proof. by case: x. Qed. | Lemma | omap_id | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [
"id"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_omap {aT rT : Type} (f g : aT -> rT) : f =1 g -> omap f =1 omap g. | Proof. by move=> Ef [?|] //=; rewrite Ef. Qed. | Lemma | eq_omap | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [
"aT"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
omapK {aT rT : Type} (f : aT -> rT) (g : rT -> aT) :
cancel f g -> cancel (omap f) (omap g). | Proof. by move=> fK [?|] //=; rewrite fK. Qed. | Lemma | omapK | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [
"aT",
"fK"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
idempotent_op (S : Type) (op : S -> S -> S) | := forall x, op x x = x. | Definition | idempotent_op | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
idempotent | := idempotent_op (only parsing). | Notation | idempotent | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [
"idempotent_op"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
idempotent_fun (U : Type) (f : U -> U) | := f \o f =1 f. | Definition | idempotent_fun | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
inr_inj {A B} : injective (@inr A B). | Proof. by move=> ? ? []. Qed. | Lemma | inr_inj | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
inl_inj {A B} : injective (@inl A B). | Proof. by move=> ? ? []. Qed. | Lemma | inl_inj | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
taggedK {I : Type} (T_ : I -> Type) (s : {i : I & T_ i}) :
Tagged T_ (tagged s) = s. | Proof. by case: s. Qed. | Lemma | taggedK | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
swap_pair {T1 T2 : Type} (x : T1 * T2) | := (x.2, x.1). | Definition | swap_pair | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
swap_pairK {T1 T2 : Type} : @cancel _ (T1 * T2) swap_pair swap_pair. | Proof. by case. Qed. | Lemma | swap_pairK | boot | boot/ssrfun.v | [
"mathcomp",
"ssreflect",
"Corelib",
"ssrfun",
"ssrnotations"
] | [
"swap_pair"
] | Note that this lemma coudn't be an instance of the [involutive] predicate. | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
"m + n" | := (plus m n) : coq_nat_scope. | Notation | m + n | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"m - n" | := (minus m n) : coq_nat_scope. | Notation | m - n | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"m * n" | := (mult m n) : coq_nat_scope. | Notation | m * n | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"m <= n" | := (le m n) : coq_nat_scope. | Notation | m <= n | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [
"le"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"m < n" | := (lt m n) : coq_nat_scope. | Notation | m < n | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [
"lt"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"m >= n" | := (ge m n) : coq_nat_scope. | Notation | m >= n | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [
"ge"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"m > n" | := (gt m n) : coq_nat_scope. | Notation | m > n | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [
"gt"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
succn | := Datatypes.S. | Notation | succn | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [] | a local bound variable. | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
predn | := Peano.pred. | Notation | predn | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"n .+1" | := (succn n) (left associativity, format "n .+1") : nat_scope. | Notation | n .+1 | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [
"succn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"n .+2" | := n.+1.+1 (left associativity, format "n .+2") : nat_scope. | Notation | n .+2 | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"n .+3" | := n.+2.+1 (left associativity, format "n .+3") : nat_scope. | Notation | n .+3 | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"n .+4" | := n.+2.+2 (left associativity, format "n .+4") : nat_scope. | Notation | n .+4 | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
"n .-1" | := (predn n) (left associativity, format "n .-1") : nat_scope. | Notation | n .-1 | boot | boot/ssrnat.v | [
"Corelib",
"PosDef",
"HB",
"structures",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"NatTrec"
] | [
"predn"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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