phanerozoic/Coq-Jasmin · Datasets at Hugging Face

fact stringlengths 8 29k	type stringclasses 20 values	library stringclasses 1 value	imports listlengths 0 9	filename stringclasses 173 values	symbolic_name stringlengths 1 44
find (T : Type) (x : T) (xs : seq T) (i:nat). #[export]	Class	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	find
find0 (T : Type) (x : T) (xs : seq T) : find x (x :: xs) 0 := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	find0
findS (T : Type) (x : T) (y : T) (ys : seq T) i {_: find x ys i} : find x (y :: ys) i.+1 \| 1 := { }. (* -------------------------------------------------------------------- *)	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	findS
closed (T : Type) (xs : seq T). #[export]	Class	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	closed
closed_nil T : closed (T:=T) nil := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	closed_nil
closed_cons T (x : T) (xs : seq T) {_: closed xs} : closed (x :: xs) := { }. (* -------------------------------------------------------------------- *)	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	closed_cons
reify (R : ringType) (a : R) (t : PExpr Z) (e : seq R). #[export]	Class	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify
reify_zero (R : ringType) e : @reify R 0 0%S e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify_zero
reify_one (R : ringType) e : @reify R 1 1%S e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify_one
reify_natconst (R : ringType) n e : @reify R n%:R ((n : Z)%:S)%S e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify_natconst
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 := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify_add
reify_opp (R : ringType) a t e {_: @reify R a t e} : reify (-a) (-t)%S e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify_opp
reify_natmul (R : ringType) a n t e {_: @reify R a t e} : reify (a + n) (t (n : Z)%:S)%S e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify_natmul
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 := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify_mul
reify_exp (R : ringType) a n t e {_: @reify R a t e} : reify (a ^+ n) (t ^+ n)%S e \| 1 := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify_exp
reify_var (R : ringType) a i e `{find R a e i} : reify a ('X_i)%S e \| 100 := { }.	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify_var
reifyl (R : ringType) a t e {_: @reify R a t e} `{closed (T := R) e} := (t, e). (* -------------------------------------------------------------------- *)	Definition	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reifyl
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	reify
freify (F : fieldType) (a : F) (t : FExpr Z) (e : seq F). #[export]	Class	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify
freify_zero (F : fieldType) e : @freify F 0 0%F e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_zero
freify_one (F : fieldType) e : @freify F 1 1%F e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_one
freify_natconst (F : fieldType) n e : @freify F n%:R ((n : Z)%:S)%F e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_natconst
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 := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_add
freify_opp (F : fieldType) a t e {_: @freify F a t e} : freify (-a) (-t)%F e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_opp
freify_natmul (F : fieldType) a n t e {_: @freify F a t e} : freify (a + n) (t (n : Z)%:S)%F e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_natmul
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 := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_mul
freify_inv (F : fieldType) a t e {_: @freify F a t e} : freify (a^-1) (t^-1)%F e := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_inv
freify_exp (F : fieldType) a n t e {_: @freify F a t e} : freify (a ^+ n) (t ^+ n)%F e \| 1 := { }. #[export]	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_exp
freify_var (F : fieldType) a i e `{find F a e i} : freify a ('X_i)%F e \| 100 := { }.	Instance	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify_var
freifyl (F : fieldType) a t e {_: @freify F a t e} `{closed (T := F) e} := (t, e). (* -------------------------------------------------------------------- *)	Definition	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freifyl
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	freify
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. Arguments R_of_Z [R].	Definition	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	R_of_Z
z0E : 0%Z = 0. Proof. by []. Qed.	Lemma	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	z0E
zaddE (z1 z2 : Z): (z1 + z2)%Z = z1 + z2. Proof. by []. Qed.	Lemma	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	zaddE
zoppE (z : Z): (-z)%Z = -z. Proof. by []. Qed.	Lemma	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	zoppE
zmulE (z1 z2 : Z): (z1 * z2)%Z = z1 * z2. Proof. by []. Qed.	Lemma	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	zmulE
zE := (z0E, zaddE, zoppE).	Definition	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	zE
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_le_incl/Z.leb_le. by move/wlog; rewrite Z.add_comm addrC. case: z1 z2=> [\|n1\|n1] [\|n2\|n2] //= _; rewrite ?(addr0, add0r) //. + by rewrite Pos2Nat.inj_add natrD. + case: (Z.compare_spec n1 n2) => [[->]\|\|]. * by rewrite Z.pos_sub_diag addrC subrr. * move=> lt; rewrite (Z.pos_sub_gt _ _ lt) /=. rewrite (Pos2Nat.inj_sub _ _ lt) natrB 1?addrC //. apply/leP/Pos2Nat.inj_le/Pos.lt_le_incl/Pos.ltb_lt. by rewrite Pos2Z.inj_ltb; apply/Pos.ltb_lt. * move=> lt; rewrite (Z.pos_sub_lt _ _ lt) /=. rewrite (Pos2Nat.inj_sub _ _ lt) natrB ?opprB 1?addrC //. apply/leP/Pos2Nat.inj_le/Pos.lt_le_incl/Pos.ltb_lt. by rewrite Pos2Z.inj_ltb; apply/Pos.ltb_lt. + by rewrite Pos2Nat.inj_add natrD opprD. by move=> z1 z2 /=; rewrite addm oppm. Qed. HB.instance Definition _ (R : ringType) := GRing.isAdditive.Build _ _ (R_of_Z (R:=R)) (R_of_Z_is_additive R).	Lemma	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	R_of_Z_is_additive
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. HB.instance Definition _ (R : ringType) := GRing.isMultiplicative.Build _ _ (R_of_Z (R:=R)) (R_of_Z_is_multiplicative R). Local Notation REeval := (@PEeval _ 0 +%R *%R (fun x y => x - y) -%R Z R_of_Z nat nat_of_N (@GRing.exp _)).	Lemma	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	R_of_Z_is_multiplicative
RE (R : ringType): @ring_eq_ext R +%R *%R -%R (@eq R). Proof. by split; do! move=> ? _ <-. Qed. Local Notation "~%R" := (fun x y => x - y). Local Notation "/%R" := (fun x y => x / y). Local Notation "^-1%R" := (@GRing.inv _) (only parsing).	Lemma	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	RE
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	RR
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	RZ
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	PN
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	RF
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	Rcorrect
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	Fcorrect
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 n) \| (pe1 * pe2)%S => match pe2 with \| ((Zpos n)%:S)%S => (Reval l pe1) + (nat_of_P n) \| _ => (Reval l pe1) (Reval l pe2) end end. Local Notation RevalC R := (PEeval 0 1 +%R *%R ~%R -%R (R_of_Z (R := R)) nat_of_N (@GRing.exp R)).	Fixpoint	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	Reval
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	PEReval
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 n) \| (pe^-1)%F => (Feval l pe)^-1 \| (pe1 / pe2)%F => (Feval l pe1) / (Feval l pe2) \| (pe1 * pe2)%F => match pe2 with \| ((Zpos n)%:S)%F => (Feval l pe1) + (nat_of_P n) \| _ => (Feval l pe1) (Feval l pe2) end end. Local Notation FevalC R := (FEeval 0 1 +%R *%R ~%R -%R /%R ^-1%R (R_of_Z (R := R)) nat_of_N (@GRing.exp R)).	Fixpoint	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	Feval
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	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	PEFeval
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 (Coq.setoid_ring.Ring_polynom.PEc 0%Z) I); vm_compute;exact (erefl true). (* -------------------------------------------------------------------- *)	Ltac	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	ssring
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 (Field_theory.FEc 0) I [::] (erefl [::])); move/(_ _ (erefl _) _ (erefl _) (erefl true)); rewrite !PEFeval; apply=> /=; do? split; cbv delta[BinPos.Pos.to_nat] => /= {xt xe}; try (exact I \|\| apply/eqP).	Ltac	proofs	[ "From HB Require Import structures.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrnat ssrfun seq.", "From mathcomp Require Import choice ssralg bigop.", "From mathcomp Require Export word_ssrZ.", "From Coq Require Import NArith ZArith BinPos Ring_polynom Field_theory." ]	proofs/3rdparty/ssrring.v	ssfield
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	pair_inj
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc_cat
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc_mem'
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	InP
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	mem_uniq_assoc
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc_mem_dom'
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 by constructor; case=> /esym. by apply/negbTE; apply/contra: t_notin_s => /(map_f fst). Qed.	Lemma	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assocP
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc_mem
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc_mem_dom
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. Qed.	Lemma	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc_inj
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc_mapE
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc_filterI
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	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	assoc_filter
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' => //; congruence. Qed.	Lemma	proofs	[ "From Coq Require List.", "From Coq Require Import Utf8.", "From mathcomp Require Import ssreflect eqtype ssrbool ssrfun ssrnat.", "From mathcomp Require Export seq." ]	proofs/3rdparty/xseq.v	in_map
ToString (t: ltype) (T: Type) := { category : string (* Name of the "register" used to print errors. *) ; _finC : finTypeC T ; to_string : T -> string }. #[global]	Class	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	ToString
Instance _finC.	Existing	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	Instance
rtype {t T} `{ToString t T} := t. (* This type and the field check_CAimm is not very elegant, but it is the only solution I have to keep a decidable equality over the type arg_kind. If new architecture need new checker for immediate then we should add an entry here. But it definition can be done in the architecture itself *) #[only(eqbOK)] derive	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	rtype
caimm_checker_s := \| CAimmC_none \| CAimmC_arm_shift_amout of shift_kind \| CAimmC_arm_wencoding of expected_wencoding \| CAimmC_arm_0_8_16_24 \| CAimmC_riscv_12bits_signed \| CAimmC_riscv_5bits_unsigned. HB.instance Definition _ := hasDecEq.Build caimm_checker_s caimm_checker_s_eqb_OK. (* -------------------------------------------------------------------- ) ( Basic architecture declaration. * Parameterized by types for registers, extra registers, flags, and conditions. *)	Inductive	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	caimm_checker_s
arch_decl (reg regx xreg rflag cond : Type) := { reg_size : wsize (* Register size. Also used as pointer size. ) ; xreg_size : wsize ( Extended registers size. *) ; cond_eqC : eqTypeC cond ; toS_r : ToString (lword reg_size) reg ; toS_rx : ToString (lword reg_size) regx ; toS_x : ToString (lword xreg_size) xreg ; toS_f : ToString lbool rflag ; reg_size_neq_xreg_size : reg_size != xreg_size ; ad_rsp : reg ; ad_fcp : FlagCombinationParams ; check_CAimm : caimm_checker_s -> forall ws, word ws -> bool }. #[global]	Class	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	arch_decl
Instances cond_eqC toS_r toS_rx toS_x toS_f ad_fcp. #[export]	Existing	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	Instances
arch_pd `{arch_decl} : PointerData := { Uptr := reg_size }. #[export]	Instance	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	arch_pd
arch_msfsz `{arch_decl} : MSFsize := { msf_size := reg_size }.	Instance	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	arch_msfsz
mk_ptr `{arch_decl} name := {\| vtype := aword Uptr; vname := name; \|}. (* FIXME ARM : Try to not use this projection *)	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	mk_ptr
reg_t {reg regx xreg rflag cond} `{arch : arch_decl reg regx xreg rflag cond} := reg.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	reg_t
regx_t {reg regx xreg rflag cond} `{arch : arch_decl reg regx xreg rflag cond} := regx.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	regx_t
xreg_t {reg regx xreg rflag cond} `{arch : arch_decl reg regx xreg rflag cond} := xreg.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	xreg_t
rflag_t {reg regx xreg rflag cond} `{arch : arch_decl reg regx xreg rflag cond} := rflag.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	rflag_t
cond_t {reg regx xreg rflag cond} `{arch : arch_decl reg regx xreg rflag cond} := cond.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	cond_t
sem_lt t := (sem_t (eval_ltype t)).	Notation	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	sem_lt
sem_olt t := (sem_ot (eval_ltype t)).	Notation	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	sem_olt
sem_lprod ts tr := (sem_prod (map eval_ltype ts) tr).	Notation	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	sem_lprod
sem_ltuple ts := (sem_tuple (map eval_ltype ts)).	Notation	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	sem_ltuple
sem_lforall P tin := (sem_forall P (map eval_ltype tin)).	Notation	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	sem_lforall
interp_safe_cond_lty tin id_safe id_semi := (values.interp_safe_cond_ty (tin := map eval_ltype tin) id_safe id_semi).	Notation	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	interp_safe_cond_lty
lreg := lword reg_size.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	lreg
wreg := sem_lt lreg.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	wreg
lxreg := lword xreg_size.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	lxreg
wxreg := sem_lt lxreg.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	wxreg
lword_reg_neq_xreg : lreg != lxreg. Proof. apply/eqP. move=> []. apply/eqP. exact: reg_size_neq_xreg_size. Qed. (* -------------------------------------------------------------------- ) ( Addresses. * An address consists of * - A displacement (an immediate value). * - A base (a register). * - A scale. * - An offset (a register). * The effective address is displacement + base + offset * scale. *)	Lemma	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	lword_reg_neq_xreg
reg_address : Type := mkAddress { ad_disp : pointer ; ad_base : option reg_t ; ad_scale : nat ; ad_offset : option reg_t }.	Record	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	reg_address
address := \| Areg of reg_address (* Absolute address. ) \| Arip of pointer. ( Address relative to instruction pointer. *)	Variant	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	address
oeq_reg (x y:option reg_t) := @eq_op (option ceqT_eqType) x y.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	oeq_reg
reg_address_beq (addr1: reg_address) addr2 := match addr1, addr2 with \| mkAddress d1 b1 s1 o1, mkAddress d2 b2 s2 o2 => [&& d1 == d2, oeq_reg b1 b2, s1 == s2 & oeq_reg o1 o2] end.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	reg_address_beq
reg_address_eq_axiom : Equality.axiom reg_address_beq. Proof. case=> [d1 b1 s1 o1] [d2 b2 s2 o2]; apply: (iffP idP) => /=. + by case/and4P ; do 4! move/eqP=> ->. by case; do 4! move=> ->; rewrite /oeq_reg !eqxx. Qed. HB.instance Definition _ := hasDecEq.Build reg_address reg_address_eq_axiom. (* -------------------------------------------------------------------- *)	Lemma	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	reg_address_eq_axiom
address_beq (addr1: address) addr2 := match addr1, addr2 with \| Areg ra1, Areg ra2 => ra1 == ra2 \| Arip p1, Arip p2 => p1 == p2 \| _, _ => false end.	Definition	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	address_beq
address_eq_axiom : Equality.axiom address_beq. Proof. by case=> []? []? /=; (constructor \|\| apply: reflect_inj eqP => ?? []). Qed. HB.instance Definition _ := hasDecEq.Build address address_eq_axiom. (* -------------------------------------------------------------------- ) ( Arguments to assembly instructions. *)	Lemma	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	address_eq_axiom
asm_arg : Type := \| Condt of cond_t \| Imm ws of word ws \| Reg of reg_t \| Regx of regx_t \| Addr of address \| XReg of xreg_t.	Variant	proofs	[ "From elpi.apps Require Import derive.", "From HB Require Import structures.", "From mathcomp Require Import ssreflect ssrfun ssrbool ssrnat eqtype ssralg.", "From mathcomp Require Import word_ssrZ." ]	proofs/arch/arch_decl.v	asm_arg

find (T : Type) (x : T) (xs : seq T) (i:nat). #[export]

Class

proofs