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[Merged by Bors] - feat(group_theory/subgroup/basic): Contrapositive of card_le_one_iff_eq_bot #9918

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3 changes: 3 additions & 0 deletions src/group_theory/subgroup/basic.lean
Original file line number Diff line number Diff line change
Expand Up @@ -479,6 +479,9 @@ end
(λ x hx, by simpa [subtype.ext_iff] using fintype.card_le_one_iff.1 h ⟨x, hx⟩ 1),
λ h, by simp [h]⟩

@[to_additive] lemma one_lt_card_iff_ne_bot [fintype H] : 1 < fintype.card H ↔ H ≠ ⊥ :=
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I was curious what to_additive does with the naming on things like this, and it turns out, it's not great. Not a problem for this PR, but I'll open an issue.

lt_iff_not_ge'.trans (not_iff_not.mpr H.card_le_one_iff_eq_bot)

/-- The inf of two subgroups is their intersection. -/
@[to_additive "The inf of two `add_subgroups`s is their intersection."]
instance : has_inf (subgroup G) :=
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