Dataset Viewer
Auto-converted to Parquet Duplicate
statement
stringlengths
1
2.66k
proof
stringlengths
0
48.4k
type
stringclasses
20 values
symbolic_name
stringlengths
1
58
library
stringclasses
6 values
filename
stringclasses
179 values
imports
listlengths
1
54
deps
listlengths
0
64
docstring
stringclasses
646 values
source_url
stringclasses
1 value
commit
stringclasses
1 value
simpm
:= Monoid.simpm.
Notation
simpm
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"c %:S"
:= (PEc c) : ssring.
Notation
c %:S
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssring" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"''X_' i"
:= (PEX _ i) : ssring.
Notation
''X_' i
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssring" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x + y"
:= (PEadd x y) : ssring.
Notation
x + y
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssring" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x - y"
:= (PEsub x y) : ssring.
Notation
x - y
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssring" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"- x"
:= (PEopp x ) : ssring.
Notation
- x
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssring" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x * y"
:= (PEmul x y) : ssring.
Notation
x * y
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssring" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x ^+ n"
:= (PEpow x n) : ssring.
Notation
x ^+ n
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssring" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"0"
:= PEO : ssring.
Notation
0
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssring" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"1"
:= PEI : ssring.
Notation
1
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssring" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"c %:S"
:= (FEc c) : ssfield.
Notation
c %:S
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"''X_' i"
:= (@FEX _ i) : ssfield.
Notation
''X_' i
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x + y"
:= (FEadd x y) : ssfield.
Notation
x + y
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x - y"
:= (FEsub x y) : ssfield.
Notation
x - y
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"- x"
:= (FEopp x ) : ssfield.
Notation
- x
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x * y"
:= (FEmul x y) : ssfield.
Notation
x * y
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x ^-1"
:= (FEinv x) : ssfield.
Notation
x ^-1
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x / y"
:= (FEdiv x y) : ssfield.
Notation
x / y
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"x ^+ n"
:= (FEpow x n) : ssfield.
Notation
x ^+ n
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"0"
:= FEO : ssfield.
Notation
0
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"1"
:= FEI : ssfield.
Notation
1
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "ssfield" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
Z_of_nat : nat >-> Z.
Coercion
Z_of_nat
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
N_of_nat : nat >-> N.
Coercion
N_of_nat
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
P_of_succ_nat : nat >-> positive.
Coercion
P_of_succ_nat
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
Z.pos : positive >-> Z.
Coercion
Z
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
find (T : Type) (x : T) (xs : seq T) (i:nat).
Class
find
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
find0 (T : Type) (x : T) (xs : seq T) : find x (x :: xs) 0
:= { }.
Instance
find0
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "find" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
findS (T : Type) (x : T) (y : T) (ys : seq T) i {_: find x ys i} : find x (y :: ys) i.+1 | 1
:= { }.
Instance
findS
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "find" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
closed (T : Type) (xs : seq T).
Class
closed
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
closed_nil T : closed (T:=T) nil
:= { }.
Instance
closed_nil
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "closed" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
closed_cons T (x : T) (xs : seq T) {_: closed xs} : closed (x :: xs)
:= { }.
Instance
closed_cons
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "closed" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify (R : ringType) (a : R) (t : PExpr Z) (e : seq R).
Class
reify
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify_zero (R : ringType) e : @reify R 0 0%S e
:= { }.
Instance
reify_zero
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify_one (R : ringType) e : @reify R 1 1%S e
:= { }.
Instance
reify_one
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify_natconst (R : ringType) n e : @reify R n%:R ((n : Z)%:S)%S e
:= { }.
Instance
reify_natconst
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify_add (R : ringType) a1 a2 t1 t2 e {_: @reify R a1 t1 e} {_: @reify R a2 t2 e} : reify (a1 + a2) (t1 + t2)%S e
:= { }.
Instance
reify_add
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify_opp (R : ringType) a t e {_: @reify R a t e} : reify (-a) (-t)%S e
:= { }.
Instance
reify_opp
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify_natmul (R : ringType) a n t e {_: @reify R a t e} : reify (a *+ n) (t * (n : Z)%:S)%S e
:= { }.
Instance
reify_natmul
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify_mul (R : ringType) a1 a2 t1 t2 e {_: @reify R a1 t1 e} {_: @reify R a2 t2 e} : reify (a1 * a2) (t1 * t2)%S e
:= { }.
Instance
reify_mul
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify_exp (R : ringType) a n t e {_: @reify R a t e} : reify (a ^+ n) (t ^+ n)%S e | 1
:= { }.
Instance
reify_exp
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify_var (R : ringType) a i e `{find R a e i} : reify a ('X_i)%S e | 100
:= { }.
Instance
reify_var
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "find", "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reifyl (R : ringType) a t e {_: @reify R a t e} `{closed (T := R) e}
:= (t, e).
Definition
reifyl
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "closed", "reify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
reify xt xe
:= match goal with |- ?a = 0 => match eval red in (reifyl (a := a)) with | (?t, ?e) => pose xt := t; pose xe := e end end.
Ltac
reify
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "reifyl" ]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify (F : fieldType) (a : F) (t : FExpr Z) (e : seq F).
Class
freify
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_zero (F : fieldType) e : @freify F 0 0%F e
:= { }.
Instance
freify_zero
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_one (F : fieldType) e : @freify F 1 1%F e
:= { }.
Instance
freify_one
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_natconst (F : fieldType) n e : @freify F n%:R ((n : Z)%:S)%F e
:= { }.
Instance
freify_natconst
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_add (F : fieldType) a1 a2 t1 t2 e {_: @freify F a1 t1 e} {_: @freify F a2 t2 e} : freify (a1 + a2) (t1 + t2)%F e
:= { }.
Instance
freify_add
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_opp (F : fieldType) a t e {_: @freify F a t e} : freify (-a) (-t)%F e
:= { }.
Instance
freify_opp
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_natmul (F : fieldType) a n t e {_: @freify F a t e} : freify (a *+ n) (t * (n : Z)%:S)%F e
:= { }.
Instance
freify_natmul
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_mul (F : fieldType) a1 a2 t1 t2 e {_: @freify F a1 t1 e} {_: @freify F a2 t2 e} : freify (a1 * a2) (t1 * t2)%F e
:= { }.
Instance
freify_mul
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_inv (F : fieldType) a t e {_: @freify F a t e} : freify (a^-1) (t^-1)%F e
:= { }.
Instance
freify_inv
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_exp (F : fieldType) a n t e {_: @freify F a t e} : freify (a ^+ n) (t ^+ n)%F e | 1
:= { }.
Instance
freify_exp
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify_var (F : fieldType) a i e `{find F a e i} : freify a ('X_i)%F e | 100
:= { }.
Instance
freify_var
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "find", "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freifyl (F : fieldType) a t e {_: @freify F a t e} `{closed (T := F) e}
:= (t, e).
Definition
freifyl
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "closed", "freify" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
freify xt xe
:= match goal with |- ?a = 0 => match eval red in (freifyl (a := a)) with | (?t, ?e) => pose xt := t; pose xe := e end end.
Ltac
freify
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "freifyl" ]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
R_of_Z (R : ringType) (z : Z) : R
:= match z with | Z0 => 0 | Zpos n => (nat_of_P n)%:R | Zneg n => - (nat_of_P n)%:R end.
Definition
R_of_Z
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "Zpos" ]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
z0E: 0%Z = 0.
Proof. by []. Qed.
Lemma
z0E
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
zaddE (z1 z2 : Z): (z1 + z2)%Z = z1 + z2.
Proof. by []. Qed.
Lemma
zaddE
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
zoppE (z : Z): (-z)%Z = -z.
Proof. by []. Qed.
Lemma
zoppE
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
zmulE (z1 z2 : Z): (z1 * z2)%Z = z1 * z2.
Proof. by []. Qed.
Lemma
zmulE
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
zE
:= (z0E, zaddE, zoppE).
Definition
zE
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "z0E", "zaddE", "zoppE" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
R_of_Z_is_additive (R : ringType): additive (R_of_Z (R := R)).
Proof. have oppm: {morph (R_of_Z (R := R)) : x / -x >-> -x}. by case=> [|n|n] //=; rewrite ?(oppr0, opprK). have addm z1 z2: R_of_Z (z1 + z2) = R_of_Z z1 + R_of_Z z2 :> R. wlog: z1 z2 / (z1 <=? z2)%Z; first move=> wlog. + case: (boolP (z1 <=? z2))%Z; first by move/wlog. + move/negbTE/Z.leb_gt/Z.lt_l...
Lemma
R_of_Z_is_additive
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "R_of_Z", "apply", "compare_spec", "lt" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
R_of_Z_is_multiplicative (R : ringType): multiplicative (R_of_Z (R := R)).
Proof. split=> //=; case=> [|z1|z1] [|z2|z2] //=; rewrite ?simpm // ?(mulNr, mulrN, opprK); by rewrite nat_of_P_mult_morphism natrM. Qed.
Lemma
R_of_Z_is_multiplicative
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "R_of_Z", "simpm" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
REeval
:= (@PEeval _ 0 +%R *%R (fun x y => x - y) -%R Z R_of_Z nat nat_of_N (@GRing.exp _)).
Notation
REeval
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "R_of_Z" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
RE (R : ringType): @ring_eq_ext R +%R *%R -%R (@eq R).
Proof. by split; do! move=> ? _ <-. Qed.
Lemma
RE
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "eq" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"~%R"
:= (fun x y => x - y).
Notation
~%R
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"/%R"
:= (fun x y => x / y).
Notation
/%R
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
"^-1%R"
:= (@GRing.inv _) (only parsing).
Notation
^-1%R
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "inv" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
RR (R : comRingType): @ring_theory R 0 1 +%R *%R ~%R -%R (@eq R).
Proof. split=> //=; [ exact: add0r | exact: addrC | exact: addrA | exact: mul1r | exact: mulrC | exact: mulrA | exact: mulrDl | exact: subrr ]. Qed.
Lemma
RR
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "eq" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
RZ (R : ringType): ring_morph (R := R) 0 1 +%R *%R ~%R -%R eq 0%Z 1%Z Zplus Zmult Zminus Z.opp Z.eqb (@R_of_Z _).
Proof. split=> //=. + by move=> x y; rewrite rmorphD. + by move=> x y; rewrite rmorphB. + by move=> x y; rewrite rmorphM. + by move=> x; rewrite raddfN. + by move=> x y /Z.eqb_eq ->. Qed.
Lemma
RZ
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "R_of_Z", "eq" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
PN (R : ringType): @power_theory R 1 *%R eq nat nat_of_N (@GRing.exp R).
Proof. split=> r [|n] //=; elim: n => //= p ih. + by rewrite Pos2Nat.inj_xI exprS -!ih -exprD addnn -mul2n. + by rewrite Pos2Nat.inj_xO -!ih -exprD addnn -mul2n. Qed.
Lemma
PN
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "eq" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
RF (F : fieldType): @field_theory F 0 1 +%R *%R ~%R -%R /%R ^-1%R (@eq F).
Proof. split=> //=; first by apply RR. + by apply/eqP; rewrite oner_eq0. + by move=> x /eqP nz_z; rewrite mulVf. Qed.
Lemma
RF
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "RR", "apply", "eq" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
Rcorrect (R : comRingType)
:= ring_correct (Eqsth R) (RE R) (Rth_ARth (Eqsth R) (RE R) (RR R)) (RZ R) (PN R) (triv_div_th (Eqsth R) (RE R) (Rth_ARth (Eqsth R) (RE R) (RR R)) (RZ R)).
Definition
Rcorrect
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "PN", "RE", "RR", "RZ" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
Fcorrect (F : fieldType)
:= Field_correct (Eqsth F) (RE F) (congr1 GRing.inv) (F2AF (Eqsth F) (RE F) (RF F)) (RZ F) (PN F) (triv_div_th (Eqsth F) (RE F) (Rth_ARth (Eqsth F) (RE F) (RR F)) (RZ F)).
Definition
Fcorrect
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "PN", "RE", "RF", "RR", "RZ", "inv" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
Reval (R : ringType) (l : seq R) (pe : PExpr Z)
:= match pe with | 0%S => 0 | 1%S => 1 | (c%:S)%S => R_of_Z c | ('X_j)%S => BinList.nth 0 j l | (pe1 + pe2)%S => (Reval l pe1) + (Reval l pe2) | (pe1 - pe2)%S => (Reval l pe1) - (Reval l pe2) | (- pe1)%S => - (Reval l pe1) | (pe1 ^+ n)%S => (Reval l pe1) ^+ (nat_of_N...
Fixpoint
Reval
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "R_of_Z", "Zpos" ]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
RevalC R
:= (PEeval 0 1 +%R *%R ~%R -%R (R_of_Z (R := R)) nat_of_N (@GRing.exp R)).
Notation
RevalC
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "R_of_Z" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
PEReval (R : ringType): RevalC _ =2 @Reval R.
Proof. move=> l; elim => //=; try by do? move=> ?->. + move=> pe1 -> pe2 ->; case: pe2 => //=. by case=> [|c|c] //=; rewrite mulr_natr. Qed.
Lemma
PEReval
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "Reval", "RevalC" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
Feval (F : fieldType) (l : seq F) (pe : FExpr Z)
:= match pe with | 0%F => 0 | 1%F => 1 | (c%:S)%F => R_of_Z c | ('X_j)%F => BinList.nth 0 j l | (pe1 + pe2)%F => (Feval l pe1) + (Feval l pe2) | (pe1 - pe2)%F => (Feval l pe1) - (Feval l pe2) | (- pe1)%F => - (Feval l pe1) | (pe1 ^+ n)%F => (Feval l pe1) ^+ (nat_of_N...
Fixpoint
Feval
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "R_of_Z", "Zpos" ]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
FevalC R
:= (FEeval 0 1 +%R *%R ~%R -%R /%R ^-1%R (R_of_Z (R := R)) nat_of_N (@GRing.exp R)).
Notation
FevalC
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "R_of_Z" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
PEFeval (F : fieldType): FevalC _ =2 @Feval F.
Proof. move=> l; elim => //=; try by do? move=> ?->. + move=> pe1 -> pe2 ->; case: pe2 => //=. by case=> [|c|c] //=; rewrite mulr_natr. Qed.
Lemma
PEFeval
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "Feval", "FevalC" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
ssring
:= let xt := fresh "xt" in let xe := fresh "xe" in apply/eqP; rewrite -subr_eq0; apply/eqP; reify xt xe; apply (@Rcorrect _ 100 xe [::] xt (@PEc _ 0%Z) I); vm_compute;exact (erefl true).
Ltac
ssring
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "Rcorrect", "apply", "reify" ]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
ssfield
:= let xt := fresh "xt" in let xe := fresh "xe" in apply/eqP; rewrite -subr_eq0; apply/eqP; (* rewrite ?(mulr0, mul0r, mulr1, mul1r); *) freify xt xe; move: (@Fcorrect _ 100 xe [::] xt (@FEc _ 0) I [::] (erefl [::])); move/(_ _ (erefl _) _ (erefl _) (erefl true)); rewrite !PEFeval; apply...
Ltac
ssfield
3rdparty
proofs/3rdparty/ssrring.v
[ "HB", "structures", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrnat", "ssrfun", "seq", "choice", "ssralg", "bigop", "word_ssrZ", "GRing.Theory", "Coq", "NArith", "ZArith", "BinPos", "Ring_polynom", "Field_theory" ]
[ "Fcorrect", "PEFeval", "apply", "freify" ]
--------------------------------------------------------------------
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
pair_inj {A B: Type} {a a': A} {b b': B} (e: (a, b) = (a', b')) : a = a' ∧ b = b'
:= let 'Logic.eq_refl := e in conj Logic.eq_refl Logic.eq_refl.
Definition
pair_inj
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "eq_refl" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc (s : seq (T * U)) (x : T) : option U
:= if s is (y, v) :: s then if x == y then Some v else assoc s x else None.
Fixpoint
assoc
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc_cat (s1 s2: seq (T * U)) x : assoc (s1 ++ s2) x = if assoc s1 x is Some _ then assoc s1 x else assoc s2 x.
Proof. by elim: s1 => [|[t u] s1 ih] //=; case: eqP. Qed.
Lemma
assoc_cat
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "assoc" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc_mem' (T: eqType) U (s: seq (T * U)) x w : assoc s x = Some w → List.In (x, w) s.
Proof. elim: s => // [ [t u] s ] ih /=; case: eqP; last by auto. by move => a /Some_inj; left; f_equal. Qed.
Lemma
assoc_mem'
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "assoc" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
InP (T: eqType) (s: seq T) m : reflect (List.In m s) (m \in s).
Proof. elim: s. by constructor. move => a s ih. rewrite in_cons. case: (@eqP _ m a). by constructor; left. case ih; constructor. by right. simpl; intuition. Qed.
Lemma
InP
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
mem_uniq_assoc (T: eqType) U (s: seq (T * U)) x w : List.In (x, w) s → uniq (map fst s) → assoc s x = Some w.
Proof. elim: s => // [ [t u] s] ih [ /pair_inj [] -> -> | rec ] /andP [nr un] /=. by rewrite eq_refl; eauto. case: eqP; last by eauto. fold (List.In (x, w) s) in rec. apply (List.in_map fst), (rwP (InP _ _)) in rec. move=> ?; subst. rewrite rec in nr. done. Qed.
Lemma
mem_uniq_assoc
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "InP", "apply", "assoc", "eq_refl", "fold", "in_map", "map", "pair_inj" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc_mem_dom' (T: eqType) U (s : seq (T * U)) x w : assoc s x = Some w -> x \in [seq v.1 | v <- s].
Proof. move => h; apply assoc_mem' in h. apply (rwP (InP _ _)), List.in_map_iff. eexists; split. 2: eassumption. reflexivity. Qed.
Lemma
assoc_mem_dom'
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "InP", "apply", "assoc", "assoc_mem'" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assocP (s : seq (T * U)) (x : T) (w : U) : uniq (map fst s) -> reflect (assoc s x = Some w) ((x, w) \in s).
Proof. elim: s => [|[t u] s ih] => uq; first by constructor. move: uq => /andP[/= t_notin_s /ih {ih}]; move: t_notin_s. case: eqP=> [->|/eqP ne_xt] t_notin_s; last first. + by rewrite in_cons eqE /= (negbTE ne_xt). rewrite inE eqE /= eqxx /=; case: eqP => [->|ne_wu] _ /=. + by constructor. suff ->: (t, w) \in s = false...
Lemma
assocP
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "apply", "assoc", "map" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc_mem (s : seq (T * U)) x w : assoc s x = Some w -> (x, w) \in s.
Proof. elim: s => [|[t u] s ih] //=; case: eqP => [-> [->]|/eqP ne]. + by rewrite in_cons eqxx orTb. by rewrite in_cons eqE /= (negbTE ne). Qed.
Lemma
assoc_mem
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "assoc" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc_mem_dom (s : seq (T * U)) x w : assoc s x = Some w -> w \in [seq v.2 | v <- s].
Proof. by move/assoc_mem/(map_f snd). Qed.
Lemma
assoc_mem_dom
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "assoc", "assoc_mem" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc_inj (s : seq (T * U)) x y w : uniq [seq v.2 | v <- s] -> assoc s x = Some w -> assoc s y = Some w -> x = y.
Proof. elim: s => [|[t u] s ih] //= /andP[u_notin_s uq_s xw yx]. move: xw yx ih u_notin_s; case: eqP => [-> [->]|ne_xt]. + by case: eqP=> [->//|] ne_yt yw _ /negbTE; rewrite (assoc_mem_dom yw). move=> xw; case: eqP=> [-> [->] _|]. + by move/negbTE; rewrite (assoc_mem_dom xw). by move=> ne_yt yw ih u_notin_s; apply: ih....
Lemma
assoc_inj
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "apply", "assoc", "assoc_mem_dom" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc_mapE m n : (∀ n u, (h (n, u)).1 = n) → assoc (map h m) n = omap (λ u, (h (n, u)).2) (assoc m n).
Proof. move => E. elim: m => // - [] t u m /= ->. case htu: h (E t u) => [ ? v ] /= ?; subst. case: eqP => //= ->. by rewrite htu. Qed.
Lemma
assoc_mapE
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "assoc", "map", "omap" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc_filterI (m: seq (T * U)) (n: T) : assoc [seq x <- m | p x.1 ] n = if p n then assoc m n else None.
Proof. elim: m n. - by move => n /=; case: ifP. case => t u m ih n /=. case: ifP. - by move => /=; case: eqP => // -> ->. by case: eqP => // -> {n} h; rewrite ih h. Qed.
Lemma
assoc_filterI
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "assoc" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
assoc_filter (m: seq (T * U)) (n: T) : p n → assoc [seq x <- m | p x.1] n = assoc m n.
Proof. by move => h; rewrite assoc_filterI h. Qed.
Corollary
assoc_filter
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "assoc", "assoc_filterI" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
in_map b m : reflect (exists2 a : A, List.In a m & b = f a) (b \in [seq f i | i <- m]).
Proof. elim: m; first by constructor => - [] _ []. move => a m ih /=. rewrite in_cons; case: eqP => [ -> | neq ] /=. - by constructor; exists a => //; left. case: ih => ih; constructor. - by case: ih => a' ??; exists a' => //; right. case => a' ha' ?; apply: ih; exists a' => //. case: ha' => //; congrue...
Lemma
in_map
3rdparty
proofs/3rdparty/xseq.v
[ "Coq", "List", "Utf8", "mathcomp", "ssreflect", "eqtype", "ssrbool", "ssrfun", "ssrnat", "seq" ]
[ "apply" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
ToString (t: ltype) (T: Type)
:= { category : string (* Name of the "register" used to print errors. *) ; _finC : finTypeC T ; to_string : T -> string }.
Class
ToString
arch
proofs/arch/arch_decl.v
[ "elpi.apps", "derive.std", "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "ssrnat", "eqtype", "ssralg", "word_ssrZ", "Coq", "Relation_Operators", "Utf8", "global", "label", "memory_model", "oseq", "sem_type", "strings", "syscall", "utils", "expr", "...
[ "finTypeC" ]
String representation of architecture components. * ToString is a class for types that have a string representation and a * particular ltype, such as registers (represented as "RAX", "RSP", etc. * with lword U64 being the associated ltype) or flags (represented as "CF", * "ZF", with lbool the associated ltype).
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
rtype {t T} `{ToString t T}
:= t.
Definition
rtype
arch
proofs/arch/arch_decl.v
[ "elpi.apps", "derive.std", "HB", "structures", "mathcomp", "ssreflect", "ssrfun", "ssrbool", "ssrnat", "eqtype", "ssralg", "word_ssrZ", "Coq", "Relation_Operators", "Utf8", "global", "label", "memory_model", "oseq", "sem_type", "strings", "syscall", "utils", "expr", "...
[ "ToString" ]
https://github.com/jasmin-lang/jasmin
3b7f334b37b917c75cc22b7c0ab686f20f89bccb
End of preview. Expand in Data Studio

Coq-Jasmin

Structured dataset from Jasmin — High-assurance cryptography language and compiler.

Source

Schema

Column Type Description
statement string Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof
proof string Verbatim proof/body, empty if the declaration has none
type string Declaration keyword
symbolic_name string Declaration identifier
library string Sub-library
filename string Repository-relative source path
imports list[string] File-level Require/Import modules
deps list[string] Intra-corpus identifiers referenced
docstring string Preceding documentation comment, empty if absent
source_url string Upstream repository
commit string Upstream commit extracted

Statistics

  • Entries: 9,644
  • With proof: 9,467 (98.2%)
  • With docstring: 938 (9.7%)
  • Libraries: 6

By type

Type Count
Lemma 4,381
Definition 3,502
Notation 443
Let 413
Instance 194
Fixpoint 180
Record 102
Variant 86
Parameter 84
Hypothesis 69
Class 51
Ltac 44
Canonical 20
Corollary 19
Inductive 16
Coercion 11
Theorem 10
Remark 9
Axiom 5
Hypotheses 5

Example

findS (T : Type) (x : T) (y : T) (ys :  seq T) i
 {_: find x ys i}
 : find x (y :: ys) i.+1 | 1
:= { }.
  • type: Instance | symbolic_name: findS | proofs/3rdparty/ssrring.v

Use

Each declaration is split into a statement (signature/claim) and a proof (body) that are disjoint and together form the complete declaration, for proof modeling, autoformalization, retrieval, and dependency analysis via deps.

Citation

@misc{coq_jasmin_dataset,
  title  = {Coq-Jasmin},
  author = {Norton, Charles},
  year   = {2026},
  note   = {Extracted from https://github.com/jasmin-lang/jasmin, commit 3b7f334b37b9},
  url    = {https://huggingface.co/datasets/phanerozoic/Coq-Jasmin}
}
Downloads last month
19

Collection including phanerozoic/Coq-Jasmin