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being trivial is invariant under iso #2206

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Jan 29, 2025
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being trivial is invariant under iso #2206

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10 changes: 10 additions & 0 deletions theories/Algebra/Groups/Subgroup.v
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Original file line number Diff line number Diff line change
Expand Up @@ -612,6 +612,16 @@ Proof.
1,2: apply istrivial_iff_grp_iso_trivial; exact _.
Defined.

Definition istrivial_grp_iso {G H : Group} (J : Subgroup G) (K : Subgroup H)
(e : subgroup_group J $<~> subgroup_group K)
: IsTrivialGroup J -> IsTrivialGroup K.
Proof.
intros triv.
apply istrivial_iff_grp_iso_trivial in triv.
apply istrivial_iff_grp_iso_trivial.
exact (triv $oE e^-1$).
Defined.

(** ** Maximal Subgroups *)

(** Every group is a (maximal) subgroup of itself. *)
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