statement stringlengths 1 4.33k | proof stringlengths 0 37.9k | type stringclasses 25
values | symbolic_name stringlengths 1 67 | library stringclasses 10
values | filename stringclasses 112
values | imports listlengths 2 138 | deps listlengths 0 64 | docstring stringclasses 798
values | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
Peval_subI l P j Q :
(forall l P, Peval l (Psub P Q) = Peval l P - Peval l Q) ->
Peval l (PsubI Q j P) = Peval l P - Peval l (Pinj j Q). | Proof.
move=> PevalB; elim: P j l => [c | j' Q' IH | P IHP i Q' IHQ'] j l /=.
- by rewrite Peval_mkPinj PevalDC PevalN addrC.
- move: (Zint_pos_sub (pos_nat_Pos_to_nat j') (pos_nat_Pos_to_nat j)).
case: ZintP => [//| _ /eqP+ _ | k nk _ /[swap] | k nk _ /[swap] ].
+ rewrite subr_eq0 => /eqP[]/Pos_to_natI->.
by r... | Lemma | Peval_subI | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"NegzE",
"Peval",
"PevalB",
"PevalDC",
"PevalN",
"Peval_mkPinj",
"Pos_to_natD",
"Pos_to_natE",
"Pos_to_natI",
"Pos_to_nat_gt0",
"Psub",
"PsubI",
"ZintP",
"Zint_pos_sub",
"add1n",
"addnC",
"addrA",
"addrC",
"apply",
"double0",
"env_jump",
"env_jumpD",
"eqr_opp",
"ltn_dou... | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_subX l P P' i' :
(forall l P, Peval l (Psub P P') = Peval l P - Peval l P') ->
Peval l (PsubX P' i' P) = Peval l P - Peval l (PX P' i' P0). | Proof.
rewrite /= rmorph0 addr0 addrC.
move=> PevalB; elim: P i' l => [c | j Q' IH | P IHP i Q' IHQ'] i' l /=.
- by rewrite PevalN mulNr.
- case: j => [j | j |]/=; rewrite PevalN mulNr -?env_jumpD//.
congr (_ + Peval (env_jump _ l) _).
apply: Pos_to_natI; rewrite !Pos_to_natE add1n prednK//.
by rewrite -double0 l... | Lemma | Peval_subX | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"NegzE",
"P0",
"Peval",
"PevalB",
"PevalN",
"Peval_mkPX",
"Pos_to_natD",
"Pos_to_natE",
"Pos_to_natI",
"Pos_to_nat_gt0",
"Psub",
"PsubX",
"ZintP",
"Zint_pos_sub",
"add1n",
"addnC",
"addr0",
"addrA",
"addrC",
"apply",
"double0",
"env_jump",
"env_jumpD",
"eqr_opp",
"exp... | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PevalB l P P' : Peval l (Psub P P') = Peval l P - Peval l P'. | Proof.
elim: P' l P => [c | j' Q' IH | P' IHP' i' Q' IHQ'] l P /=.
- by rewrite PevalBC.
- by rewrite Peval_subI.
case: P => [c | j Q | P i Q] /=.
- by rewrite PevalDC addrA addrC !PevalN mulNr -opprD.
- rewrite opprD addrCA -mulNr.
case: j => [j | j |] /=; rewrite PevalN IHQ'/= -?env_jumpD//.
congr (_ + (Peval (en... | Lemma | PevalB | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"NegzE",
"Peval",
"PevalBC",
"PevalDC",
"PevalN",
"Peval_mkPX",
"Peval_subI",
"Peval_subX",
"Pos_to_natD",
"Pos_to_natE",
"Pos_to_natI",
"Pos_to_nat_gt0",
"Psub",
"ZintP",
"Zint_pos_sub",
"add1n",
"addr0",
"addrA",
"addrACA",
"addrC",
"addrCA",
"apply",
"double0",
"env_... | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Meval | := (Meval
1 *%R N.to_nat (@GRing.exp R) (@env_jump R) env_nth). | Notation | Meval | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"env_jump",
"env_nth",
"exp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
cMeval | := (cMeval
1 *%R N.to_nat (@GRing.exp R) R_of_C (@env_jump R) env_nth). | Notation | cMeval | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"env_jump",
"env_nth",
"exp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
CFactor | := (CFactor 0 eq_op cdiv). | Notation | CFactor | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
MFactor | := (MFactor 0 1 eq_op cdiv). | Notation | MFactor | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
POneSubst | := (POneSubst 0 1 +%R *%R eq_op cdiv). | Notation | POneSubst | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PNSubst1 | := (PNSubst1 0 1 +%R *%R eq_op cdiv). | Notation | PNSubst1 | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PNSubst | := (PNSubst 0 1 +%R *%R eq_op cdiv). | Notation | PNSubst | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PSubstL1 | := (PSubstL1 0 1 +%R *%R eq_op cdiv). | Notation | PSubstL1 | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PSubstL | := (PSubstL 0 1 +%R *%R eq_op cdiv). | Notation | PSubstL | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PNSubstL | := (PNSubstL 0 1 +%R *%R eq_op cdiv). | Notation | PNSubstL | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Mon_of_Pol | := (Mon_of_Pol 0 eq_op). | Notation | Mon_of_Pol | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Meval_mkZmon l j M : Meval l (mkZmon j M) = Meval l (zmon j M). | Proof. by case: M. Qed. | Lemma | Meval_mkZmon | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Meval"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Meval_zmon_pred l j M :
Meval (env_jump 1 l) (zmon_pred j M) = Meval l (zmon j M). | Proof.
case: j => [p | p |//]; rewrite ?Meval_mkZmon/= -?env_jumpD//.
congr (Meval (env_jump _ l) M); apply: Pos_to_natI.
by rewrite !Pos_to_natE add1n prednK// double_gt0 Pos_to_nat_gt0.
Qed. | Lemma | Meval_zmon_pred | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Meval",
"Meval_mkZmon",
"Pos_to_natE",
"Pos_to_natI",
"Pos_to_nat_gt0",
"add1n",
"apply",
"double_gt0",
"env_jump",
"env_jumpD",
"prednK"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Meval_mkVmon l i M :
Meval l (mkVmon i M) = Meval l M * env_nth 1 l ^+ Pos.to_nat i. | Proof.
case: M => [//| j M | i' M] /=; rewrite ?Meval_zmon_pred//.
by rewrite Pos_to_natD addnC exprD mulrA.
Qed. | Lemma | Meval_mkVmon | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Meval",
"Meval_zmon_pred",
"Pos_to_natD",
"addnC",
"env_nth",
"exprD",
"mulrA"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_CFactor l P c : let (Q, R) := CFactor P c in
Peval l P = Peval l Q + R_of_C c * Peval l R. | Proof.
elim: P l => [c' | j P IH | P IHP i Q IHQ] l /=.
- by case: cdiv (cdivP c' c) => q r -> /=; rewrite rmorphD rmorphM addrC.
- by case: CFactor (IH (env_jump j l)) => R' S /=; rewrite !Peval_mkPinj.
case: CFactor (IHP l) => R1 S1 ->.
case: CFactor (IHQ (env_jump 1 l)) => R2 S2 ->.
by rewrite !Peval_mkPX mulrDr mul... | Lemma | Peval_CFactor | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"CFactor",
"Peval",
"Peval_mkPX",
"Peval_mkPinj",
"R1",
"R2",
"S1",
"S2",
"addrACA",
"addrC",
"env_jump",
"mulrA",
"mulrDl",
"mulrDr",
"rmorphD",
"rmorphM"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Meval_MFactor l P c M : let (Q, R) := MFactor P c M in
Peval l P = Peval l Q + cMeval l (c, M) * Peval l R. | Proof.
rewrite /cMeval; elim: P l M => [c'|j P IH|P IHP i Q IHQ] l [|jM M|iM M]/=.
- case: eqP => [->|_] /=; first by rewrite rmorph0 rmorph1 add0r !mul1r.
by case: cdiv (cdivP c' c) => q r -> /=; rewrite rmorphD rmorphM mulr1 addrC.
- by rewrite rmorph0 mulr0 addr0.
- by rewrite rmorph0 mulr0 addr0.
- case: eqP => [... | Lemma | Meval_MFactor | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"CFactor",
"MFactor",
"Meval_mkZmon",
"Meval_zmon_pred",
"Peval",
"Peval_CFactor",
"Peval_mkPX",
"Peval_mkPinj",
"Pos_to_natB",
"Pos_to_natD",
"Pos_to_natI",
"R1",
"R2",
"S1",
"S2",
"add",
"add0r",
"addr0",
"addrAC",
"addrACA",
"addrC",
"apply",
"cMeval",
"env_jump",
... | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_POneSubst l P1 cM1 P2 P3 : POneSubst P1 cM1 P2 = Some P3 ->
cMeval l cM1 = Peval l P2 -> Peval l P1 = Peval l P3. | Proof.
case: cM1 => cc M1 /=; case: MFactor (Meval_MFactor l P1 cc M1) => Q1 R1 -> eP3.
suff -> : P3 = Padd Q1 (Pmul P2 R1) by rewrite PevalD PevalM => <-.
by case: R1 eP3 => [c |? ?|? ? ?]; [case: eqP => [//|_]| |]; move=> -[].
Qed. | Lemma | Peval_POneSubst | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"MFactor",
"Meval_MFactor",
"P1",
"POneSubst",
"Padd",
"Peval",
"PevalD",
"PevalM",
"Pmul",
"R1",
"cMeval",
"cc"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_PNSubst1 l n P1 cM1 P2 : cMeval l cM1 = Peval l P2 ->
Peval l P1 = Peval l (PNSubst1 P1 cM1 P2 n). | Proof.
by elim: n P1 => [|n IHn] /= P1;
case: POneSubst (@Peval_POneSubst l P1 cM1 P2) => // P eP eOS;
rewrite -?IHn//; apply: eP.
Qed. | Lemma | Peval_PNSubst1 | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"P1",
"PNSubst1",
"POneSubst",
"Peval",
"Peval_POneSubst",
"apply",
"cMeval"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_PNSubst l n P1 cM1 P2 P3 : PNSubst P1 cM1 P2 n = Some P3 ->
cMeval l cM1 = Peval l P2 -> Peval l P1 = Peval l P3. | Proof.
rewrite /PNSubst; case: POneSubst (@Peval_POneSubst l P1 cM1 P2) => // P.
by case: n => [//|n] /(_ P erefl) + [<-] ?; rewrite -Peval_PNSubst1//; apply.
Qed. | Lemma | Peval_PNSubst | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"P1",
"PNSubst",
"POneSubst",
"Peval",
"Peval_PNSubst1",
"Peval_POneSubst",
"apply",
"cMeval"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_PSubstL1 l n LM1 P1 :
all (fun MP => cMeval l MP.1 == Peval l MP.2) LM1 ->
Peval l P1 = Peval l (PSubstL1 P1 LM1 n). | Proof.
elim: LM1 P1 => [//|[M2 P2] LM2 IH] /= P1 /andP[/eqP eMP2 aLM2].
by rewrite -IH// -Peval_PNSubst1.
Qed. | Lemma | Peval_PSubstL1 | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"P1",
"PSubstL1",
"Peval",
"Peval_PNSubst1",
"all",
"cMeval"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_PSubstL l n LM1 P1 P2 : PSubstL P1 LM1 n = Some P2 ->
all (fun MP => cMeval l MP.1 == Peval l MP.2) LM1 ->
Peval l P1 = Peval l P2. | Proof.
elim: LM1 P1 => [//|[M2 P2'] LM2 IH] /= P3 + /andP[/eqP M2P2' a].
case: PNSubst (@Peval_PNSubst l n P3 M2 P2') => [P /(_ P erefl) eP|_].
- by move=> -[<-]; rewrite -Peval_PSubstL1// eP.
- by move=> ?; apply: IH.
Qed. | Lemma | Peval_PSubstL | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"P1",
"PNSubst",
"PSubstL",
"Peval",
"Peval_PNSubst",
"Peval_PSubstL1",
"all",
"apply",
"cMeval"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_PNSubstL l m n LM1 P1 :
all (fun MP => cMeval l MP.1 == Peval l MP.2) LM1 ->
Peval l P1 = Peval l (PNSubstL P1 LM1 m n). | Proof.
by elim: m LM1 P1 => [|m IHm] LM1 P1 a /=;
case: PSubstL (@Peval_PSubstL l n LM1 P1) => // P /(_ P erefl);
rewrite -?IHm//; apply.
Qed. | Lemma | Peval_PNSubstL | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"P1",
"PNSubstL",
"PSubstL",
"Peval",
"Peval_PSubstL",
"all",
"apply",
"cMeval"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Meval_Mon_of_Pol l P m : Mon_of_Pol P = Some m ->
cMeval l m = Peval l P. | Proof.
case: m => c M; elim: P l c M => [c' | j P IH | P IHP i Q IHQ] l c M /=.
- by case: eqP => [//|_] [<- <-]; rewrite /cMeval/= mulr1.
- case: Mon_of_Pol IH => // -[{}c {}M] /[swap] -[<- <-].
by rewrite /cMeval Meval_mkZmon/=; apply.
rewrite -[match Q with Pc _ => _ | _ => _ end]/(Peq Q P0).
case: Peq (@Peval_Peq... | Lemma | Meval_Mon_of_Pol | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Meval_mkVmon",
"Meval_mkZmon",
"Mon_of_Pol",
"P0",
"Peq",
"Peval",
"Peval_Peq",
"addr0",
"apply",
"cMeval",
"env_jump",
"mulr1",
"mulrA",
"rmorph0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
cMeval | := (cMeval
1 *%R N.to_nat (@GRing.exp R) R_of_C (@env_jump R) (env_nth 0)). | Notation | cMeval | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"env_jump",
"env_nth",
"exp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval | := (PEeval 0 1 +%R *%R +%R id
N.to_nat (@GRing.exp R) R_of_C (env_nth 0)). | Notation | PEeval | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"env_nth",
"exp",
"id"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval_eqs | := (PEeval_eqs true andb 0 1 +%R *%R +%R id
N.to_nat (@GRing.exp R) eq_op R_of_C (env_nth 0)). | Notation | PEeval_eqs | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"env_nth",
"exp",
"id"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Pol_of_PExpr | := (Pol_of_PExpr 0 1 +%R *%R +%R id eq_op). | Notation | Pol_of_PExpr | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"id"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mk_monpol_list | := (mk_monpol_list
0 1 +%R *%R +%R id eq_op cdiv). | Notation | mk_monpol_list | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"id"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
norm_subst | := (norm_subst 0 1 +%R *%R +%R id eq_op cdiv). | Notation | norm_subst | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"id"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ring_checker | := (ring_checker 0 1 +%R *%R +%R id eq_op cdiv). | Notation | ring_checker | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"id"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sPeval_Pol_of_PExpr l pe : Peval l (Pol_of_PExpr pe) = PEeval l pe. | Proof.
elim: pe l => [||//|i|e1 IH1 e2 IH2|e1 IH1 e2 IH2|e1 IH1 e2 IH2|e IH|e IH k]l/=.
- by rewrite rmorph0.
- by rewrite rmorph1.
- exact: Peval_mkX.
- by move: e1 IH1 => [||c|i|e1' e2'|e1' e2'|e1' e2'|e|e k] IH1;
move: e2 IH2 => [||c'|i'|e1'' e2''|e1'' e2''|e1'' e2''|e'|e' k'] IH2;
rewrite ?Psub_add ?PevalD ... | Lemma | sPeval_Pol_of_PExpr | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval",
"Peval",
"PevalD",
"PevalM",
"Peval_mkX",
"Peval_pow_N",
"Pol_of_PExpr",
"Popp_id",
"Psub_add",
"addrC",
"e'",
"rmorph0",
"rmorph1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sMeval_mk_monpol_list l lpe :
all (fun PP => PEeval l PP.1 == PEeval l PP.2) lpe ->
all (fun MP => cMeval l MP.1 == Peval l MP.2) (mk_monpol_list lpe). | Proof.
elim: lpe => [//| [pe1 pe2] lpe IH] /=/andP[/eqP pe12 a].
have := @Meval_Mon_of_Pol _ _ R_of_C l (norm_subst 0 [::] pe1).
case: Mon_of_Pol; rewrite /= IH// => -[c M] /(_ _ erefl)->.
by rewrite !sPeval_Pol_of_PExpr pe12 andbT.
Qed. | Lemma | sMeval_mk_monpol_list | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Meval_Mon_of_Pol",
"Mon_of_Pol",
"PEeval",
"Peval",
"all",
"cMeval",
"mk_monpol_list",
"norm_subst",
"sPeval_Pol_of_PExpr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sPeval_norm_subst n l lpe pe :
all (fun PP => PEeval l PP.1 == PEeval l PP.2) lpe ->
Peval l (norm_subst n (mk_monpol_list lpe) pe) = PEeval l pe. | Proof.
move/sMeval_mk_monpol_list/Peval_PNSubstL => <-//.
exact: sPeval_Pol_of_PExpr.
Qed. | Lemma | sPeval_norm_subst | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval",
"Peval",
"Peval_PNSubstL",
"all",
"mk_monpol_list",
"norm_subst",
"sMeval_mk_monpol_list",
"sPeval_Pol_of_PExpr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sPEeval_eqs_PEeval l lpe :
PEeval_eqs l lpe -> all (fun PP => PEeval l PP.1 == PEeval l PP.2) lpe. | Proof.
elim: lpe => [//|[pe1 pe2] lpe IH] /= elpe.
by case: lpe elpe IH => [->//|? ?] /andP[-> ?] ->.
Qed. | Lemma | sPEeval_eqs_PEeval | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval",
"PEeval_eqs",
"all"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
sCring_checkerT n l lpe pe1 pe2 :
PEeval_eqs l lpe ->
ring_checker n lpe pe1 pe2 ->
PEeval l pe1 = PEeval l pe2. | Proof.
move/sPEeval_eqs_PEeval => elpe /(Peval_Peq R_of_C l).
by rewrite !sPeval_norm_subst.
Qed. | Lemma | sCring_checkerT | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval",
"PEeval_eqs",
"Peval_Peq",
"ring_checker",
"sPEeval_eqs_PEeval",
"sPeval_norm_subst"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval_eqs | := (PEeval_eqs true andb 0 1 +%R *%R
(fun x y : R => x - y) -%R N.to_nat (@GRing.exp R) eq_op R_of_C (env_nth 0)). | Notation | PEeval_eqs | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"env_nth",
"exp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
mk_monpol_list | := (mk_monpol_list
0 1 +%R *%R (fun x y : C => x - y) -%R eq_op cdiv). | Notation | mk_monpol_list | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
norm_subst | := (norm_subst
0 1 +%R *%R (fun x y : C => x - y) -%R eq_op cdiv). | Notation | norm_subst | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ring_checker | := (ring_checker
0 1 +%R *%R (fun x y : C => x - y) -%R eq_op cdiv). | Notation | ring_checker | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_Pol_of_PExpr l pe : Peval l (Pol_of_PExpr pe) = PEeval l pe. | Proof.
elim: pe l => [||//|i|e1 IH1 e2 IH2|e1 IH1 e2 IH2|e1 IH1 e2 IH2|e IH|e IH k]l/=.
- by rewrite rmorph0.
- by rewrite rmorph1.
- exact: Peval_mkX.
- by move: e1 IH1 => [||c|i|e1' e2'|e1' e2'|e1' e2'|e|e k] IH1;
move: e2 IH2 => [||c'|i'|e1'' e2''|e1'' e2''|e1'' e2''|e'|e' k'] IH2;
rewrite ?PevalD ?IH1 ?IH2/... | Lemma | Peval_Pol_of_PExpr | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval",
"Peval",
"PevalB",
"PevalD",
"PevalM",
"PevalN",
"Peval_mkX",
"Peval_pow_N",
"Pol_of_PExpr",
"addrC",
"e'",
"rmorph0",
"rmorph1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Meval_mk_monpol_list l lpe :
all (fun PP => PEeval l PP.1 == PEeval l PP.2) lpe ->
all (fun MP => cMeval l MP.1 == Peval l MP.2) (mk_monpol_list lpe). | Proof.
elim: lpe => [//| [pe1 pe2] lpe IH] /=/andP[/eqP pe12 a].
have := @Meval_Mon_of_Pol _ _ R_of_C l (norm_subst 0 [::] pe1).
case: Mon_of_Pol; rewrite /= IH// => -[c M] /(_ _ erefl)->.
by rewrite !Peval_Pol_of_PExpr pe12 andbT.
Qed. | Lemma | Meval_mk_monpol_list | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Meval_Mon_of_Pol",
"Mon_of_Pol",
"PEeval",
"Peval",
"Peval_Pol_of_PExpr",
"all",
"cMeval",
"mk_monpol_list",
"norm_subst"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Peval_norm_subst n l lpe pe :
all (fun PP => PEeval l PP.1 == PEeval l PP.2) lpe ->
Peval l (norm_subst n (mk_monpol_list lpe) pe) = PEeval l pe. | Proof.
by move/Meval_mk_monpol_list/Peval_PNSubstL => <-//; apply: Peval_Pol_of_PExpr.
Qed. | Lemma | Peval_norm_subst | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Meval_mk_monpol_list",
"PEeval",
"Peval",
"Peval_PNSubstL",
"Peval_Pol_of_PExpr",
"all",
"apply",
"mk_monpol_list",
"norm_subst"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval_eqs_PEeval l lpe :
PEeval_eqs l lpe -> all (fun PP => PEeval l PP.1 == PEeval l PP.2) lpe. | Proof.
elim: lpe => [//|[pe1 pe2] lpe IH] /= elpe.
by case: lpe elpe IH => [->//|? ?] /andP[-> ?] ->.
Qed. | Lemma | PEeval_eqs_PEeval | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval",
"PEeval_eqs",
"all"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Cring_checkerT n l lpe pe1 pe2 :
PEeval_eqs l lpe ->
ring_checker n lpe pe1 pe2 ->
PEeval l pe1 = PEeval l pe2. | Proof.
move/PEeval_eqs_PEeval => elpe /(Peval_Peq R_of_C l).
by rewrite !Peval_norm_subst.
Qed. | Lemma | Cring_checkerT | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval",
"PEeval_eqs",
"PEeval_eqs_PEeval",
"Peval_Peq",
"Peval_norm_subst",
"ring_checker"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Ctriv_divP (C : pzSemiRingType) (x y : C) :
let (q, r) := triv_div 0 1 eq_op x y in x = y * q + r. | Proof.
by rewrite /triv_div; case: eqP => [->|_]; rewrite ?addr0 ?mulr1 ?mulr0 ?add0r.
Qed. | Lemma | Ctriv_divP | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"add0r",
"addr0",
"mulr0",
"mulr1"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Pos_add_R | :=
fix add_R (x_1 x_2 : positive) (x_R : positive_R x_1 x_2)
(y_1 y_2 : positive) (y_R : positive_R y_1 y_2) {struct x_R} :
positive_R (Pos.add x_1 y_1) (Pos.add x_2 y_2) :=
match x_R with
| xI_R p_1 p_2 p_R =>
match y_R with
| xI_R q_1 q_2 q_R => xO_R (add_carry_R p_1 p_2 p_R q_1 q_2 q_R)
... | Definition | Pos_add_R | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"add"
] | Use derive.param2 when elpi supports mutual fixpoints | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
Pos_sub_mask_R | :=
fix sub_mask_R (x_1 x_2 : positive) (x_R : positive_R x_1 x_2)
(y_1 y_2 : positive) (y_R : positive_R y_1 y_2) {struct x_R} :
mask_R (Pos.sub_mask x_1 y_1) (Pos.sub_mask x_2 y_2) :=
match x_R with
| xI_R _ _ p_R =>
match y_R with
| xI_R _ _ q_R => double_mask_R (sub_mask_R _ _ p_R _ _ q_R... | Definition | Pos_sub_mask_R | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
bool_Rxx b : bool_R b b. | Proof. by case: b; constructor. Qed. | Lemma | bool_Rxx | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | a bunch of helper lemmas | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
nat_Rxx n : nat_R n n. | Proof. by elim: n => [| n IH]; constructor. Qed. | Lemma | nat_Rxx | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
positive_Rxx p : positive_R p p. | Proof. by elim: p => [p IH | p IH |]; constructor. Qed. | Lemma | positive_Rxx | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
N_Rxx n : N_R n n. | Proof. by case: n => [| p]; constructor; apply: positive_Rxx. Qed. | Lemma | N_Rxx | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"apply",
"positive_Rxx"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
bool_R_eq b b' : bool_R b b' -> b = b'. | Proof. by case: b b' => [] [] []. Qed. | Lemma | bool_R_eq | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_bool_R b b' : b = b' -> bool_R b b'. | Proof. by move=> ->; apply: bool_Rxx. Qed. | Lemma | eq_bool_R | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"apply",
"bool_Rxx"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
list_R_eq T (s s' : seq T) : list_R eq s s' -> s = s'. | Proof. by elim=> [//| x _ <- {}s _ _ <-]. Qed. | Lemma | list_R_eq | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"seq"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
positive_R_eq p p' : positive_R p p' -> p = p'. | Proof. by elim/positive_R_ind => [? ? ? ->|? ? ? ->|]. Qed. | Lemma | positive_R_eq | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
N_R_eq n n' : N_R n n' -> n = n'. | Proof. by elim/N_R_ind => [//| ? _ /positive_R_eq<-]. Qed. | Lemma | N_R_eq | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"n'",
"positive_R_eq"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
eq_bool_R2 {A B} {f : A -> B -> bool} {C D} {g : C -> D -> bool}
{AC : A -> C -> Type} {BD : B -> D -> Type} :
(forall a c (rac : AC a c) b d (rbd : BD b d), f a b = g c d) ->
forall a c (rac : AC a c) b d (rbd : BD b d), bool_R (f a b) (g c d). | Proof. by move=> e a1 a2 ra b1 b2 rb; apply/eq_bool_R/e. Qed. | Lemma | eq_bool_R2 | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"AC",
"a1",
"a2",
"apply",
"eq_bool_R"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
list_R_map A B (RAB : A -> B -> Type) (f : A -> B) :
(forall a, RAB a (f a)) -> forall l : seq A, list_R RAB l (map f l). | Proof.
move=> rf; elim=> [| a l IH]; first exact: nil_R.
by apply: cons_R; [apply: rf | apply: IH].
Qed. | Lemma | list_R_map | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"apply",
"map",
"seq"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PExpr_R_map A B (RAB : A -> B -> Type) (f : A -> B) :
(forall a, RAB a (f a)) ->
forall g : PExpr A, PExpr_R RAB g (PEmap f g). | Proof.
move=> rf; elim=> [||c|p||||g IH|g IH n]; [| | | |move=> f1 IH1 f2 IH2..| |].
- exact: PEO_R.
- exact: PEI_R.
- exact: PEc_R.
- exact/PEX_R/positive_Rxx.
- by apply: PEadd_R; [apply: IH1 | apply: IH2].
- by apply: PEsub_R; [apply: IH1 | apply: IH2].
- by apply: PEmul_R; [apply: IH1 | apply: IH2].
- exact/PEopp_R... | Lemma | PExpr_R_map | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"N_Rxx",
"apply",
"f1",
"f2",
"positive_Rxx"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
R_of_N (R : pzSemiRingType) (natr : nat -> R) (n : N) : R | :=
natr (N.to_nat n). | Definition | R_of_N | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"nat"
] | Refinement of C to N, for actual computation in the reflexive tactic. | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
R_of_N | := (R_of_N R (GRing.natmul 1)). | Notation | R_of_N | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"natmul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
R_of_N_natmul i r : Nnat i r -> R_of_N i = r%:R. | Proof. by rewrite /R_of_N => /eqP->. Qed. | Lemma | R_of_N_natmul | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Nnat",
"R_of_N"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
semiring_checker_map_N_to_nat n lpe pe1 pe2 :
ring_checker N0 (Npos xH) N.add N.mul N.add id N.eqb
(triv_div N0 (Npos xH) N.eqb) n lpe pe1 pe2
= ring_checker 0 1 +%R *%R +%R id eq_op (triv_div 0 1 eq_op) n
(map (fun pp => (PEmap N.to_nat pp.1, PEmap N.to_nat pp.2)) lpe)
(PEmap N.to_nat pe1) (PEmap N... | Proof.
by apply/bool_R_eq/(ring_checker_R _ _ NnatD NnatM NnatD _
(eq_bool_R2 Nnat_eq) (triv_div_R _ _ (eq_bool_R2 Nnat_eq)) (nat_Rxx n)) => //;
[apply: list_R_map => -[{}pe1 {}pe2]; apply: pair_R| |];
apply/PExpr_R_map/Nnat_N_to_nat.
Qed. | Lemma | semiring_checker_map_N_to_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"NnatD",
"NnatM",
"Nnat_N_to_nat",
"Nnat_eq",
"PExpr_R_map",
"add",
"apply",
"bool_R_eq",
"eq_bool_R2",
"eqb",
"id",
"list_R_map",
"map",
"mul",
"nat_Rxx",
"ring_checker"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval_map_N_to_nat l (pe : PExpr N) :
PEeval 0 1 +%R *%R +%R id N.to_nat (GRing.exp (R:=R))
(GRing.natmul 1) (env_nth 0) l (PEmap N.to_nat pe)
= PEeval 0 1 +%R *%R +%R id N.to_nat (GRing.exp (R:=R))
R_of_N (env_nth 0) l pe. | Proof. by elim: pe => //= ? -> // ? // ->. Qed. | Lemma | PEeval_map_N_to_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval",
"R_of_N",
"env_nth",
"exp",
"id",
"natmul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval_eqs_map_N_to_nat l lpe :
PEeval_eqs true andb 0 1 +%R *%R +%R id N.to_nat (GRing.exp (R:=R)) eq_op
R_of_N (env_nth 0) l lpe ->
PEeval_eqs true andb 0 1 +%R *%R +%R id N.to_nat (GRing.exp (R:=R)) eq_op
(GRing.natmul 1) (env_nth 0) l
(map (fun pp => (PEmap N.to_nat pp.1, PEmap N.to_nat pp.2)) l... | Proof.
elim: lpe => [//|[pe1 pe2] lpe IH] /=; rewrite !PEeval_map_N_to_nat.
by case: lpe IH => [_/eqP//| [pe1' pe2'] lpe] /= IH /andP[-> /IH].
Qed. | Lemma | PEeval_eqs_map_N_to_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval_eqs",
"PEeval_map_N_to_nat",
"R_of_N",
"env_nth",
"exp",
"id",
"map",
"natmul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval | := (PEeval 0 1 +%R *%R +%R id N.to_nat (@GRing.exp R)
R_of_N (env_nth 0)). | Notation | PEeval | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"R_of_N",
"env_nth",
"exp",
"id"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval_eqs | := (PEeval_eqs true andb 0 1 +%R *%R +%R id
N.to_nat (@GRing.exp R) eq_op R_of_N (env_nth 0)). | Notation | PEeval_eqs | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"R_of_N",
"env_nth",
"exp",
"id"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ring_checker | := (ring_checker
N0 (Npos xH) N.add N.mul N.add id N.eqb (triv_div N0 (Npos xH) N.eqb)). | Notation | ring_checker | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"add",
"eqb",
"id",
"mul"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Nsemiring_correct n l lpe pe1 pe2 :
PEeval_eqs l lpe ->
ring_checker n lpe pe1 pe2 ->
PEeval l pe1 = PEeval l pe2. | Proof.
rewrite semiring_checker_map_N_to_nat -!PEeval_map_N_to_nat.
by move/PEeval_eqs_map_N_to_nat; apply/sCring_checkerT/Ctriv_divP.
Qed. | Lemma | Nsemiring_correct | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Ctriv_divP",
"PEeval",
"PEeval_eqs",
"PEeval_eqs_map_N_to_nat",
"PEeval_map_N_to_nat",
"apply",
"ring_checker",
"sCring_checkerT",
"semiring_checker_map_N_to_nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
R_of_Z (R : pzRingType) (i : Z) : R | := intr (int_of_Z i). | Definition | R_of_Z | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"int_of_Z",
"intr"
] | Refinement of C to Z, for actual computation in the reflexive tactic. | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
R_of_Z_intr i r : Zint i r -> R_of_Z i = intr r. | Proof. by rewrite /R_of_Z => /eqP->. Qed. | Lemma | R_of_Z_intr | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"R_of_Z",
"Zint",
"intr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ring_checker_map_int_of_Z n lpe pe1 pe2 :
ring_checker Z0 (Zpos xH) Z.add Z.mul Z.sub Z.opp Z.eqb
(triv_div Z0 (Zpos xH) Z.eqb) n lpe pe1 pe2
= ring_checker 0 1 +%R *%R (fun x y => x - y) -%R eq_op (triv_div 0 1 eq_op) n
(map (fun pp => (PEmap int_of_Z pp.1, PEmap int_of_Z pp.2)) lpe)
(PEmap int_of_... | Proof.
by apply/bool_R_eq/(ring_checker_R _ _ ZintD ZintM ZintB ZintN
(eq_bool_R2 Zint_eq) (triv_div_R _ _ (eq_bool_R2 Zint_eq)) (nat_Rxx n)) => //;
[apply: list_R_map => -[{}pe1 {}pe2]; apply: pair_R| |];
apply/PExpr_R_map/Zint_int_of_Z.
Qed. | Lemma | ring_checker_map_int_of_Z | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PExpr_R_map",
"ZintB",
"ZintD",
"ZintM",
"ZintN",
"Zint_eq",
"Zint_int_of_Z",
"add",
"apply",
"bool_R_eq",
"eq_bool_R2",
"eqb",
"int_of_Z",
"list_R_map",
"map",
"mul",
"nat_Rxx",
"opp",
"ring_checker",
"sub"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval_map_int_of_Z l (pe : PExpr Z) :
PEeval 0 1 +%R *%R (fun x y => x - y) -%R N.to_nat (GRing.exp (R:=R))
intr (env_nth 0) l (PEmap int_of_Z pe)
= PEeval 0 1 +%R *%R (fun x y => x - y) -%R N.to_nat (GRing.exp (R:=R))
R_of_Z (env_nth 0) l pe. | Proof. by elim: pe => //= ? -> // ? // ->. Qed. | Lemma | PEeval_map_int_of_Z | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval",
"R_of_Z",
"env_nth",
"exp",
"int_of_Z",
"intr"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval_eqs_map_int_of_Z l lpe :
PEeval_eqs true andb 0 1 +%R *%R (fun x y => x - y) -%R N.to_nat (GRing.exp (R:=R))
eq_op R_of_Z (env_nth 0) l lpe ->
PEeval_eqs true andb 0 1 +%R *%R (fun x y => x - y) -%R N.to_nat (GRing.exp (R:=R))
eq_op intr (env_nth 0) l
(map (fun pp => (PEmap int_of_Z pp.1, PEm... | Proof.
elim: lpe => [//|[pe1 pe2] lpe IH] /=; rewrite !PEeval_map_int_of_Z.
by case: lpe IH => [_ /eqP//| [pe1' pe2'] lpe] /= IH /andP[-> /IH].
Qed. | Lemma | PEeval_eqs_map_int_of_Z | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"PEeval_eqs",
"PEeval_map_int_of_Z",
"R_of_Z",
"env_nth",
"exp",
"int_of_Z",
"intr",
"map"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval | := (PEeval 0 1 +%R *%R (fun x y => x - y) -%R
N.to_nat (@GRing.exp R) R_of_Z (env_nth 0)). | Notation | PEeval | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"R_of_Z",
"env_nth",
"exp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PEeval_eqs | := (PEeval_eqs true andb 0 1 +%R *%R (fun x y => x - y) -%R
N.to_nat (@GRing.exp R) eq_op R_of_Z (env_nth 0)). | Notation | PEeval_eqs | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"R_of_Z",
"env_nth",
"exp"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
ring_checker | := (ring_checker
Z0 (Zpos xH) Z.add Z.mul Z.sub Z.opp Z.eqb (triv_div Z0 (Zpos xH) Z.eqb)). | Notation | ring_checker | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"add",
"eqb",
"mul",
"opp",
"sub"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Zring_correct n l lpe pe1 pe2 :
PEeval_eqs l lpe ->
ring_checker n lpe pe1 pe2 ->
PEeval l pe1 = PEeval l pe2. | Proof.
rewrite ring_checker_map_int_of_Z -!PEeval_map_int_of_Z.
by move/PEeval_eqs_map_int_of_Z; apply/Cring_checkerT/Ctriv_divP.
Qed. | Lemma | Zring_correct | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Cring_checkerT",
"Ctriv_divP",
"PEeval",
"PEeval_eqs",
"PEeval_eqs_map_int_of_Z",
"PEeval_map_int_of_Z",
"apply",
"ring_checker",
"ring_checker_map_int_of_Z"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
Nat_tail_addE n m : Nat.tail_add n m = (m + n)%N. | Proof. by elim: n m => [| n IH /=] m; rewrite ?addn0// IH addSn addnS. Qed. | Lemma | Nat_tail_addE | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"addSn",
"addn0",
"addnS"
] | Some basic facts about `Decimal.uint` and `Hexadecimal.uint` | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
Nat_tail_mulE n m : Nat.tail_mul n m = (m * n)%N. | Proof.
rewrite /Nat.tail_mul -[RHS]add0n.
elim: n 0%N => [| n IH /=] r; first by rewrite muln0 addn0.
by rewrite mulnS addnA -IH Nat_tail_addE.
Qed. | Lemma | Nat_tail_mulE | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Nat_tail_addE",
"add0n",
"addn0",
"addnA",
"muln0",
"mulnS"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PosSD p : Pos.succ p = Pos.add 1 p. | Proof. by apply: Pos_to_natI; rewrite !Pos_to_natE add1n. Qed. | Lemma | PosSD | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Pos_to_natE",
"Pos_to_natI",
"add",
"add1n",
"apply"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PosDA : associative Pos.add. | Proof. by move=> ? ? ?; apply: Pos_to_natI; rewrite !Pos_to_natE addnA. Qed. | Lemma | PosDA | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Pos_to_natE",
"Pos_to_natI",
"add",
"addnA",
"apply"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
PosMC : commutative Pos.mul. | Proof. by move=> ? ?; apply: Pos_to_natI; rewrite !Pos_to_natE mulnC. Qed. | Lemma | PosMC | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Pos_to_natE",
"Pos_to_natI",
"apply",
"mul",
"mulnC"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
uint_N_nat (d : Decimal.uint) : N.to_nat (N.of_uint d) = Nat.of_uint d. | Proof.
suff acc d' p : Pos.to_nat (Pos.of_uint_acc d' p)
= Nat.of_uint_acc d' (Pos.to_nat p) by elim: d => //=.
by elim: d' p => //= d' IH p; rewrite Nat_tail_mulE;
rewrite -[10%N]/(Pos.to_nat 1~0~1~0) -!Pos_to_natE -{}IH ?PosSD?PosDA PosMC.
Qed. | Lemma | uint_N_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Nat_tail_mulE",
"PosDA",
"PosMC",
"PosSD",
"Pos_to_natE",
"of_uint",
"of_uint_acc"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
hex_uint_N_nat (d : Hexadecimal.uint) :
N.to_nat (N.of_hex_uint d) = Nat.of_hex_uint d. | Proof.
suff acc d' p : Pos.to_nat (Pos.of_hex_uint_acc d' p)
= Nat.of_hex_uint_acc d' (Pos.to_nat p) by elim: d => //=.
by elim: d' p => //= d' IH p; rewrite Nat_tail_mulE;
rewrite -[16%N]/(Pos.to_nat 1~0~0~0~0) -!Pos_to_natE -{}IH ?PosSD?PosDA PosMC.
Qed. | Lemma | hex_uint_N_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Nat_tail_mulE",
"PosDA",
"PosMC",
"PosSD",
"Pos_to_natE",
"of_hex_uint",
"of_hex_uint_acc"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
N_to_natS i : N.to_nat (N.succ i) = (N.to_nat i).+1. | Proof. by case: i => [//| p /=]; rewrite Pos_to_natS. Qed. | Lemma | N_to_natS | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Pos_to_natS"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
addn_expand | := Eval compute in addn. | Definition | addn_expand | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"addn"
] | expanding versions of the `N -> nat` conversion. ` | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
nat_of_pos_rec_expand (p : positive) (a : nat) : nat | :=
match p with
| p0~1 => addn_expand a (nat_of_pos_rec_expand p0 (addn_expand a a))
| p0~0 => nat_of_pos_rec_expand p0 (addn_expand a a)
| 1 => a
end%positive. | Fixpoint | nat_of_pos_rec_expand | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"addn_expand",
"nat",
"p0"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat_of_pos_expand (p : positive) : nat | := nat_of_pos_rec_expand p 1. | Definition | nat_of_pos_expand | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"nat",
"nat_of_pos_rec_expand"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat_of_N_expand (n : N) : nat | :=
if n is Npos p then nat_of_pos_expand p else 0%N. | Definition | nat_of_N_expand | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"nat",
"nat_of_pos_expand"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
nat_of_N_expandE : nat_of_N_expand = N.to_nat. | Proof. by []. Qed. | Lemma | nat_of_N_expandE | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"nat_of_N_expand"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
add_pos_nat (p : positive) (n : nat) : nat | := Pos.iter S n p. | Definition | add_pos_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"iter",
"nat"
] | For representing input terms of the form `S (... (S n) ...)` | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
add_pos_natE p n : add_pos_nat p n = Pos.to_nat p + n. | Proof.
by elim: p n => //= p IHp n; rewrite !IHp Pos_to_natE -addnn ?[RHS]addSn addrA.
Qed. | Lemma | add_pos_natE | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"Pos_to_natE",
"addSn",
"add_pos_nat",
"addnn",
"addrA"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
large_nat | :=
| large_nat_N of N
| large_nat_uint of Number.uint
| large_nat_dec_uint of Decimal.uint
| large_nat_hex_uint of Hexadecimal.uint. | Variant | large_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [] | that use `Number.uint` | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
nat_of_large_nat (n : large_nat) : nat | :=
match n with
| large_nat_N n => nat_of_N_expand n
| large_nat_uint n => Nat.of_num_uint n
| large_nat_dec_uint n => Nat.of_uint n
| large_nat_hex_uint n => Nat.of_hex_uint n
end. | Definition | nat_of_large_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"large_nat",
"nat",
"nat_of_N_expand",
"of_hex_uint",
"of_uint"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
N_of_large_nat (n : large_nat) : N | :=
match n with
| large_nat_N n => n
| large_nat_uint n => N.of_num_uint n
| large_nat_dec_uint n => N.of_uint n
| large_nat_hex_uint n => N.of_hex_uint n
end. | Definition | N_of_large_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"large_nat",
"of_hex_uint",
"of_uint"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d | |
large_nat_N_nat (n : large_nat) :
N.to_nat (N_of_large_nat n) = nat_of_large_nat n. | Proof.
by case: n => [n|[d|h]|d|h] /=;
rewrite ?nat_of_N_expandE ?uint_N_nat ?hex_uint_N_nat.
Qed. | Lemma | large_nat_N_nat | algebra | algebra/ring_tactic.v | [
"elpi",
"derive.std",
"param2",
"micromega_plugin",
"NatDef",
"Corelib",
"IntDef",
"formula",
"witness",
"checker",
"eval",
"mathcomp",
"ssreflect",
"ssrfun",
"ssrbool",
"eqtype",
"ssrnat",
"seq",
"preorder",
"ssralg",
"ssrint",
"binnums",
"mathcomp.algebra",
"Extra",
... | [
"N_of_large_nat",
"hex_uint_N_nat",
"large_nat",
"nat_of_N_expandE",
"nat_of_large_nat",
"uint_N_nat"
] | https://github.com/math-comp/math-comp | 91d97df9cf3204b4dab84f4e24bc633e84b6473d |
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