Theorems · Theorem · group theory
AddAction.isPretransitive_iff_base
∀ {G : Type u_1} {X : Type u_2} [inst : AddGroup G] [inst_1 : AddAction G X] (a : X),
AddAction.IsPretransitive G X ↔ ∀ (x : X), ∃ g, g +ᵥ a = xAn additive action of an additive group is pretransitive iff any element can be moved from a fixed given one.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddActionstatement and proof · cited by 820
- neg_add_cancel_rightproof · cited by 75
- AddAction.IsPretransitivestatement and proof · cited by 56
- vadd_vaddproof · cited by 40
- AddAction.exists_vadd_eqproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- AddAction.IsPreprimitive.of_isTrivialBlock_of_notMem_fixedPointsproof · cited by 1
- AddAction.isPretransitive_iff_orbit_eq_univproof · cited by 0