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complete is_trivial_subgroup

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This commit is contained in:
Ulrik Buchholtz 2016-09-15 15:04:10 -04:00
parent 6cec5dcdaa
commit 22d8fad087
1 changed files with 7 additions and 1 deletions
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8
algebra/subgroup.hlean
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@ -22,6 +22,8 @@ namespace group
(Rmul : Π{g h}, R g → R h → R (g * h)) (Rmul : Π{g h}, R g → R h → R (g * h))
(Rinv : Π{g}, R g → R (g⁻¹)) (Rinv : Π{g}, R g → R (g⁻¹))
attribute subgroup_rel.R [coercion]
/-- Every group G has at least two subgroups, the trivial subgroup containing only one, and the full subgroup. --/ /-- Every group G has at least two subgroups, the trivial subgroup containing only one, and the full subgroup. --/
definition trivial_subgroup.{u} (G : Group.{u}) : subgroup_rel.{u u} G := definition trivial_subgroup.{u} (G : Group.{u}) : subgroup_rel.{u u} G :=
begin begin
@ -32,7 +34,11 @@ namespace group
{ intros g p, esimp at *, rewrite p, exact one_inv } { intros g p, esimp at *, rewrite p, exact one_inv }
end end
definition is_trivial_subgroup (G : Group) (R : subgroup_rel G) : Prop := sorry /- Π g, R g = trivial_subgroup g -/ definition is_trivial_subgroup (G : Group) (R : subgroup_rel G) : Prop :=
trunctype.mk (Π g : G, R g ↔ trivial_subgroup G g)
begin
apply pi.is_trunc_pi, intro g, apply is_trunc_prod
end
definition full_subgroup.{u} (G : Group.{u}) : subgroup_rel.{u 0} G := definition full_subgroup.{u} (G : Group.{u}) : subgroup_rel.{u 0} G :=
begin begin