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Elimination principles for GroupCoeq #2184

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Move FreeProduct_rec after FreeProduct_ind*
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jdchristensen committed Mar 15, 2025
commit dd823b02264934dba28ecd2b07a356d8a2403764
16 changes: 8 additions & 8 deletions theories/Algebra/Groups/FreeProduct.v
Original file line number Diff line number Diff line change
Expand Up @@ -724,14 +724,6 @@ Definition freeproduct_inl {G H : Group} : GroupHomomorphism G (FreeProduct G H)
Definition freeproduct_inr {G H : Group} : GroupHomomorphism H (FreeProduct G H)
:= amal_inr.

Definition FreeProduct_rec {G H K : Group} (f : G $-> K) (g : H $-> K)
: FreeProduct G H $-> K.
Proof.
snapply (AmalgamatedFreeProduct_rec _ f g).
intros [].
exact (grp_homo_unit f @ (grp_homo_unit g)^).
Defined.

Definition freeproduct_ind_hprop {G H} (P : FreeProduct G H -> Type)
`{forall x, IsHProp (P x)}
(l : forall g, P (freeproduct_inl g))
Expand All @@ -755,6 +747,14 @@ Definition equiv_freeproduct_ind_homotopy {Funext : Funext} {G H K : Group}
<~> f $== f'
:= equiv_amalgamatedfreeproduct_ind_homotopy _ _.

Definition FreeProduct_rec {G H K : Group} (f : G $-> K) (g : H $-> K)
: FreeProduct G H $-> K.
Proof.
srapply (AmalgamatedFreeProduct_rec _ f g).
intros [].
exact (grp_homo_unit f @ (grp_homo_unit g)^).
Defined.

Definition freeproduct_rec_beta_inl {G H K : Group}
(f : G $-> K) (g : H $-> K)
: FreeProduct_rec f g $o freeproduct_inl $== f
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