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Adapt to Rocq 9.4 and MathComp dev #1

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995dcae
Adapt to Rocq dev: HB `of` clauses, mathcomp Nz* hierarchy, `^*` level
JasonGross Jul 28, 2026
af4d558
Adapt to the mathcomp 2.6 ssreflect `rewrite (_ : A = B)` goal order
JasonGross Jul 28, 2026
67e0565
Relax opam bounds to Rocq 9.4+alpha and the mathcomp dev branches
JasonGross Jul 28, 2026
7b28e0e
Use Set SsrOldRewriteGoalsOrder instead of reordering the proof scripts
JasonGross Jul 28, 2026
4b6c6de
Require MathComp algebra 2.6
JasonGross Jul 28, 2026
c52d2b4
Reorder rewrite side-condition proofs
JasonGross Jul 28, 2026
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56 changes: 28 additions & 28 deletions complete_dioid.v
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Original file line number Diff line number Diff line change
Expand Up @@ -59,7 +59,7 @@ Unset Strict Implicit.
Unset Printing Implicit Defensive.

Reserved Notation "x ^+" (at level 2, format "x ^+").
Reserved Notation "x ^*" (at level 2, format "x ^*").
Reserved Notation "x ^*" (at level 1, left associativity, format "x ^*").

Local Open Scope classical_set_scope.
Local Open Scope ring_scope.
Expand All @@ -68,7 +68,7 @@ Local Open Scope dioid_scope.

Import Order.Theory GRing.Theory.

HB.mixin Record isCompleteDioid d D of Dioid d D & CompleteLattice d D := {
HB.mixin Record isCompleteDioid d D & Dioid d D & CompleteLattice d D := {
set_mulDl : forall (a : D) (B : set D),
a * set_join B = set_join [set a * x | x in B];
set_mulDr : forall (a : D) (B : set D),
Expand Down Expand Up @@ -253,7 +253,7 @@ suff Hyp : forall i, (a + 1) ^ i = set_add [set a ^ j | j in [set x | 'I_i.+1 x]
elim=> [ | i IHi]; [by rewrite set_add1 !exp0|].
rewrite expS mulrDl mul1r IHi set_mulDl.
set B' := [set a ^ j | j in [set j | (1 <= j <= i)%N]].
rewrite [X in set_join X](_ : _ = a ^ i.+1 |` B'); last first.
rewrite [X in set_join X](_ : _ = a ^ i.+1 |` B').
{ rewrite predeqP => x; split.
- move=> -[y [[j Hj] _ <-] <-].
rewrite expS /= -!expS.
Expand All @@ -263,7 +263,7 @@ rewrite [X in set_join X](_ : _ = a ^ i.+1 |` B'); last first.
move=> -[[//|j] /andP [Hj Hji] <-]; rewrite expS; exists (a ^ j) => //.
by move: Hji => /ltnW; rewrite -ltnS => Hji; exists (Ordinal Hji). }
rewrite -[set_join]/set_add set_addDl.
rewrite (_ : image _ _ = (1%R |` B')); last first.
rewrite (_ : image _ _ = (1%R |` B')).
{ rewrite predeqP => x; split.
{ move=> -[[[|j] Hj] _ <-]; [by left; rewrite exp0|].
by right; exists (Ordinal Hj). }
Expand All @@ -286,7 +286,7 @@ Lemma kleene_sqr a : a^* * a^* = a^*.
Proof.
rewrite {1}/op_kleene set_mulDr.
set B' := (a ^* |` (range (fun i => a ^ i.+1 * a ^*))).
rewrite (_ : image _ _ = B'); last first.
rewrite (_ : image _ _ = B').
{ rewrite predeqP => x; split.
- by move=> -[_ [[|i] _ <-] <-]; [left; rewrite exp0 mul1r|right; exists i].
- move=> [-> | [i _ <-]]; [by exists 1%R; [exists O|rewrite mul1r]|].
Expand All @@ -310,7 +310,7 @@ Qed.
Lemma kleene_kleene a : (a ^*) ^* = a ^*.
Proof.
rewrite kleeneSr /op_plus.
rewrite (_ : image _ _ = a ^* |` set0).
rewrite (_ : image _ _ = a ^* |` set0); last first.
by rewrite setU0 set_join1 kleeneSr addrA adddd.
rewrite predeqP => x; split.
- move=> [i _ <-]; left; exact: kleene_exp.
Expand All @@ -324,7 +324,7 @@ Theorem kleene_star_least a b : forall x, (x = a * x + b) -> a ^* * b <= x.
Proof.
move=> x Hx.
rewrite set_mulDr.
rewrite [X in set_join X](_ : _ = [set (a ^ i) * b | i in setT]); last first.
rewrite [X in set_join X](_ : _ = [set (a ^ i) * b | i in setT]).
rewrite predeqP => y; split.
- by move=> [_ [i _ <-] <-]; exists i.
- by move=> [i _ <-]; exists (a ^ i); [exists i|].
Expand Down Expand Up @@ -435,15 +435,15 @@ Notation "a / b" := (div a b) : dioid_scope.

#[short(type="comCompleteDioidType")]
HB.structure Definition ComCompleteDioid d :=
{ D of GRing.ComSemiRing D & CompleteDioid d D }.
{ D of GRing.ComNzSemiRing D & CompleteDioid d D }.

HB.factory Record isComCompleteDioid d D
of ComDioid d D & CompleteLattice d D := {
& ComDioid d D & CompleteLattice d D := {
set_mulDl : forall (a : D) (B : set D),
a * set_join B = set_join [set a * x | x in B];
}.

HB.builders Context d D of isComCompleteDioid d D.
HB.builders Context d D & isComCompleteDioid d D.
Lemma set_mulDr a (B : set D) :
set_join B * a = set_join [set x * a | x in B].
Proof.
Expand All @@ -454,7 +454,7 @@ HB.instance Definition _ := isCompleteDioid.Build d D set_mulDl set_mulDr.
HB.end.

HB.factory Record CompleteLattice_isComCompleteDioid d D
of CompleteLattice d D := {
& CompleteLattice d D := {
zero : D;
add : D -> D -> D;
one : D;
Expand All @@ -474,7 +474,7 @@ HB.factory Record CompleteLattice_isComCompleteDioid d D
mul a (set_join B) = set_join [set mul a x | x in B];
}.

HB.builders Context d D of CompleteLattice_isComCompleteDioid d D.
HB.builders Context d D & CompleteLattice_isComCompleteDioid d D.
HB.instance Definition _ := POrder_isComDioid.Build d D
addA addC add0d adddd mulA mulC mul1d mulDl mul0d oner_neq0 le_def.
HB.instance Definition _ := isComCompleteDioid.Build d D set_mulDl.
Expand Down Expand Up @@ -552,10 +552,10 @@ HB.structure Definition SubCompleteDioid d (D : completeDioidType d) S d' :=

HB.factory Record SubDioid_JoinSubCompleteLattice_isJoinSubCompleteDioid
d (D : completeDioidType d) S d' U
of @SubDioid d D S d' U & @JoinSubCompleteLattice d D S d' U := {}.
& @SubDioid d D S d' U & @JoinSubCompleteLattice d D S d' U := {}.

HB.builders Context d D S d' U
of SubDioid_JoinSubCompleteLattice_isJoinSubCompleteDioid d D S d' U.
& SubDioid_JoinSubCompleteLattice_isJoinSubCompleteDioid d D S d' U.
Lemma set_mulDl (a : U) (B : set U) :
a * set_join B = set_join [set a * x | x in B].
Proof.
Expand All @@ -573,50 +573,50 @@ HB.end.

HB.factory Record SubDioid_SubPOrder_isJoinSubCompleteDioid d
(D : completeDioidType d) S d' U
of @SubDioid d D S d' U & @Order.SubPOrder d D S d' U := {
& @SubDioid d D S d' U & @Order.SubPOrder d D S d' U := {
opredSJ_subproof : set_join_closed S;
}.

HB.builders Context d D S d' U
of SubDioid_SubPOrder_isJoinSubCompleteDioid d D S d' U.
& SubDioid_SubPOrder_isJoinSubCompleteDioid d D S d' U.
HB.instance Definition _ := SubPOrder_isJoinSubCompleteLattice.Build d D S d' U
opredSJ_subproof.
HB.instance Definition _ :=
SubDioid_JoinSubCompleteLattice_isJoinSubCompleteDioid.Build d D S d' U.
HB.end.

HB.factory Record SubChoice_isJoinSubCompleteDioid d (D : completeDioidType d)
S (d' : Order.disp_t) U of SubChoice D S U := {
S (d' : Order.disp_t) U & SubChoice D S U := {
semiring_closed_subproof : semiring_closed S;
opredSJ_subproof : set_join_closed S;
}.

HB.builders Context d D S d' U of SubChoice_isJoinSubCompleteDioid d D S d' U.
HB.builders Context d D S d' U & SubChoice_isJoinSubCompleteDioid d D S d' U.
HB.instance Definition _ := SubChoice_isSubDioid.Build d D S d' U
semiring_closed_subproof.
HB.instance Definition _ :=
SubDioid_SubPOrder_isJoinSubCompleteDioid.Build d D S d' U opredSJ_subproof.
HB.end.

HB.factory Record SubChoice_isJoinSubComCompleteDioid d
(D : comCompleteDioidType d) S (d' : Order.disp_t) U of SubChoice D S U := {
(D : comCompleteDioidType d) S (d' : Order.disp_t) U & SubChoice D S U := {
semiring_closed_subproof : semiring_closed S;
opredSJ_subproof : set_join_closed S;
}.

HB.builders Context d D S d' U
of SubChoice_isJoinSubComCompleteDioid d D S d' U.
& SubChoice_isJoinSubComCompleteDioid d D S d' U.
HB.instance Definition _ := SubChoice_isJoinSubCompleteDioid.Build d D S d' U
semiring_closed_subproof opredSJ_subproof.
HB.instance Definition _ := GRing.SubSemiRing_isSubComSemiRing.Build D S U.
HB.end.

HB.factory Record SubDioid_SubCompleteLattice_isSubCompleteDioid
d (D : completeDioidType d) S d' U
of @SubDioid d D S d' U & @SubCompleteLattice d D S d' U := {}.
& @SubDioid d D S d' U & @SubCompleteLattice d D S d' U := {}.

HB.builders Context d D S d' U
of SubDioid_SubCompleteLattice_isSubCompleteDioid d D S d' U.
& SubDioid_SubCompleteLattice_isSubCompleteDioid d D S d' U.
Lemma set_mulDl (a : U) (B : set U) :
a * set_join B = set_join [set a * x | x in B].
Proof.
Expand All @@ -634,27 +634,27 @@ HB.end.

HB.factory Record SubDioid_SubPOrder_isSubCompleteDioid d
(D : completeDioidType d) S d' U
of @SubDioid d D S d' U & @Order.SubPOrder d D S d' U := {
& @SubDioid d D S d' U & @Order.SubPOrder d D S d' U := {
opredSM_subproof : set_meet_closed S;
opredSJ_subproof : set_join_closed S;
}.

HB.builders Context d D S d' U
of SubDioid_SubPOrder_isSubCompleteDioid d D S d' U.
& SubDioid_SubPOrder_isSubCompleteDioid d D S d' U.
HB.instance Definition _ := SubPOrder_isSubCompleteLattice.Build d D S d' U
opredSM_subproof opredSJ_subproof.
HB.instance Definition _ :=
SubDioid_SubCompleteLattice_isSubCompleteDioid.Build d D S d' U.
HB.end.

HB.factory Record SubChoice_isSubCompleteDioid d (D : completeDioidType d) S
(d' : Order.disp_t) U of SubChoice D S U := {
(d' : Order.disp_t) U & SubChoice D S U := {
semiring_closed_subproof : semiring_closed S;
opredSM_subproof : set_meet_closed S;
opredSJ_subproof : set_join_closed S;
}.

HB.builders Context d D S d' U of SubChoice_isSubCompleteDioid d D S d' U.
HB.builders Context d D S d' U & SubChoice_isSubCompleteDioid d D S d' U.
HB.instance Definition _ := SubChoice_isSubDioid.Build d D S d' U
semiring_closed_subproof.
HB.instance Definition _ :=
Expand All @@ -663,14 +663,14 @@ HB.instance Definition _ :=
HB.end.

HB.factory Record SubChoice_isSubComCompleteDioid d
(D : comCompleteDioidType d) S (d' : Order.disp_t) U of SubChoice D S U := {
(D : comCompleteDioidType d) S (d' : Order.disp_t) U & SubChoice D S U := {
semiring_closed_subproof : semiring_closed S;
opredSM_subproof : set_meet_closed S;
opredSJ_subproof : set_join_closed S;
}.

HB.builders Context d D S d' U
of SubChoice_isSubComCompleteDioid d D S d' U.
& SubChoice_isSubComCompleteDioid d D S d' U.
HB.instance Definition _ := SubChoice_isSubCompleteDioid.Build d D S d' U
semiring_closed_subproof opredSM_subproof opredSJ_subproof.
HB.instance Definition _ := GRing.SubSemiRing_isSubComSemiRing.Build D S U.
Expand Down
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