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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