Theorems · Theorem · group theory
MulAction.isPretransitive_iff_orbit_eq_univ
∀ {G : Type u_1} {X : Type u_2} [inst : Group G] [inst_1 : MulAction G X] (a : X),
MulAction.IsPretransitive G X ↔ MulAction.orbit G a = Set.univAn action of a group is pretransitive iff the orbit of every given element is full
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- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Groupstatement and proof · cited by 6,238
- Set.univstatement and proof · cited by 3,945
- MulActionstatement and proof · cited by 1,294
- MulAction.orbitstatement and proof · cited by 114
- MulAction.IsPretransitivestatement · cited by 94
- Set.ext_iffproof · cited by 90
- MulAction.isPretransitive_iff_baseproof · cited by 4
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