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Adapt to Rocq#21180 #2315

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fa2fc2c
more carefully split groups
Tragicus Oct 9, 2025
872ba2d
shorter fix
Tragicus Oct 9, 2025
2a5e2c8
even shorter fix
Tragicus Oct 10, 2025
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9 changes: 8 additions & 1 deletion theories/Algebra/Groups/FreeGroup.v
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Original file line number Diff line number Diff line change
Expand Up @@ -241,7 +241,14 @@ Section Reduction.
(** Finally we have defined the free group on [A] *)
Definition FreeGroup : Group.
Proof.
snapply (Build_Group freegroup_type); repeat split; exact _.
snapply (Build_Group freegroup_type).
- exact _.
- exact _.
- exact _.
- split.
+ repeat split; exact _.
+ exact _.
+ exact _.
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@jdchristensen jdchristensen Oct 9, 2025

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I'm curious how reflexivity could possibly solve any of the goals here. That doesn't look possible to me. And it's a bit annoying to be unable to use `repeat split'.

Do either of the following work?

    snapply (Build_Group freegroup_type).
    4: repeat split.
    all: exact _.

or with the second line replaced with

    4: split.  4: split.  4: split.

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@Tragicus Tragicus Oct 9, 2025

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One of the goals is the fact that inv x is the left-inverse of x. Since the unit and the operation are not yet instantiated, there is a solution that makes op the constant operation returning the unit.
Oh, good catch, 4: repeat split causes the issue, but 4: split. 4: repeat split does work, thank you.

Defined.

Definition word_rec (G : Group) (s : A -> G) : A + A -> G.
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9 changes: 8 additions & 1 deletion theories/Algebra/Groups/FreeProduct.v
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Expand Up @@ -524,7 +524,14 @@ Section AmalgamatedFreeProduct.

Definition AmalgamatedFreeProduct : Group.
Proof.
snapply (Build_Group amal_type); repeat split; exact _.
snapply (Build_Group amal_type).
- exact _.
- exact _.
- exact _.
- split.
+ repeat split; exact _.
+ exact _.
+ exact _.
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@jdchristensen jdchristensen Oct 9, 2025

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I'd also prefer something more concise here.

Defined.

End AmalgamatedFreeProduct.
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15 changes: 8 additions & 7 deletions theories/Algebra/Groups/Group.v
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Expand Up @@ -969,17 +969,18 @@ Definition grp_prod : Group -> Group -> Group.
Proof.
intros G H.
snapply (Build_Group (G * H)).
4: repeat split.
- intros [g1 h1] [g2 h2].
exact (g1 * g2, h1 * h2).
- exact (1, 1).
- exact (functor_prod inv inv).
- exact _.
- intros x y z; apply path_prod'; apply simple_associativity.
- intros x; apply path_prod'; apply left_identity.
- intros x; apply path_prod'; apply right_identity.
- intros x; apply path_prod'; apply left_inverse.
- intros x; apply path_prod'; apply right_inverse.
- split.
+ repeat split.
* exact _.
* intros x y z; apply path_prod'; apply simple_associativity.
* intros x; apply path_prod'; apply left_identity.
* intros x; apply path_prod'; apply right_identity.
+ intros x; apply path_prod'; apply left_inverse.
+ intros x; apply path_prod'; apply right_inverse.
Defined.

(** Maps into the direct product can be built by mapping separately into each factor. *)
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59 changes: 30 additions & 29 deletions theories/Homotopy/HomotopyGroup.v
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Expand Up @@ -46,8 +46,7 @@ Instance is1functor_homotopygroup_type_ptype (n : nat)
definitionally equal to [Pi 1 (iterated_loops n X)] *)
Definition Pi1 (X : pType) : Group.
Proof.
srapply (Build_Group (Tr 0 (loops X)));
repeat split.
srapply (Build_Group (Tr 0 (loops X))).
(** Operation *)
- intros x y.
strip_truncations.
Expand All @@ -57,33 +56,35 @@ Proof.
(** Inverse *)
- srapply Trunc_rec; intro x.
exact (tr x^).
(** [IsHSet] *)
- exact _.
(** Associativity *)
- intros x y z.
strip_truncations.
cbn; apply ap.
apply concat_p_pp.
(** Left identity *)
- intro x.
strip_truncations.
cbn; apply ap.
apply concat_1p.
(** Right identity *)
- intro x.
strip_truncations.
cbn; apply ap.
apply concat_p1.
(** Left inverse *)
- intro x.
strip_truncations.
apply (ap tr).
apply concat_Vp.
(** Right inverse *)
- intro x.
strip_truncations.
apply (ap tr).
apply concat_pV.
- split.
+ repeat split.
(** [IsHSet] *)
* exact _.
(** Associativity *)
* intros x y z.
strip_truncations.
cbn; apply ap.
apply concat_p_pp.
(** Left identity *)
* intro x.
strip_truncations.
cbn; apply ap.
apply concat_1p.
(** Right identity *)
* intro x.
strip_truncations.
cbn; apply ap.
apply concat_p1.
(** Left inverse *)
+ intro x.
strip_truncations.
apply (ap tr).
apply concat_Vp.
(** Right inverse *)
+ intro x.
strip_truncations.
apply (ap tr).
apply concat_pV.
Defined.

(** Definition of the nth homotopy group *)
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