Theorems · Inductive type · group theory
AddAction.IsPretransitive
(M : Type u_5) → (α : Type u_6) → [VAdd M α] → Prop
M acts pretransitively on α if for any x y there is g such that g +ᵥ x = y.
A transitive action should furthermore have α nonempty.
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- VAdd
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- VAddstatement · cited by 616
Cited by65
Results whose statement or proof uses this declaration.
- AddAction.exists_vadd_eqstatement and proof · cited by 20
- AddAction.IsMultiplyPretransitiveproof · cited by 17
- AddAction.IsPretransitive.exists_vadd_eqstatement and proof · cited by 6
- AddAction.IsPretransitive.of_surjective_mapstatement and proof · cited by 5
- AddAction.IsPreprimitive.of_surjectiveproof · cited by 4
- AddAction.isPreprimitive_congrproof · cited by 4
- AddAction.isPretransitive_congrstatement and proof · cited by 4
- AddAction.IsBlock.ncard_block_add_ncard_orbit_eqstatement and proof · cited by 4
- AddAction.IsPretransitive.discreteTopology_iffstatement and proof · cited by 2
- AddAction.IsPretransitive.of_embedding_congrstatement · cited by 2
- AddAction.IsPretransitive.of_vadd_eqstatement and proof · cited by 2
- AddAction.isPretransitive_iff_basestatement and proof · cited by 2