Theorems · Inductive type · group theory
MulAction.IsPretransitive
(M : Type u_5) → (α : Type u_6) → [SMul M α] → Prop
M acts pretransitively on α if for any x y there is g such that g • x = y.
A transitive action should furthermore have α nonempty.
- Cited by
- 94 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- SMul
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by105
Results whose statement or proof uses this declaration.
- MulAction.IsMultiplyPretransitiveproof · cited by 33
- MulAction.exists_smul_eqstatement and proof · cited by 32
- MulAction.IsPretransitive.exists_smul_eqstatement and proof · cited by 12
- MulAction.IsPreprimitive.of_surjectiveproof · cited by 8
- MulAction.is_one_pretransitive_iffstatement · cited by 7
- MulAction.IsPretransitive.of_surjective_mapstatement and proof · cited by 7
- MulAction.isPreprimitive_congrproof · cited by 6
- SubMulAction.ofStabilizer.isMultiplyPretransitivestatement and proof · cited by 5
- MulAction.IsBlock.ncard_block_mul_ncard_orbit_eqstatement and proof · cited by 4
- MulAction.isCoatom_stabilizer_iff_preprimitivestatement and proof · cited by 4
- MulAction.isPretransitive_congrstatement and proof · cited by 4
- MulAction.isPretransitive_iff_basestatement and proof · cited by 4