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Theorems · Theorem · group theory

AddAction.IsPretransitive.exists_vadd_eq

∀ {M : Type u_5} {α : Type u_6} {inst : VAdd M α} [self : AddAction.IsPretransitive M α] (x y : α), ∃ g, g +ᵥ x = y

There is g such that g +ᵥ x = y.

Defined in
Mathlib.Algebra.Group.Action.Pretransitive
Cited by
6 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Assumes
AddAction.IsPretransitive
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AddAction.exists_vadd_eq · cited by 20AddAction.exists_vadd_eqAddAction.IsPretransitive.of_surjective_map · cited by 5IsPretransitive.of_surjec…AddAction.isPretransitive_congr · cited by 4AddAction.isPretransitive…SubAddAction.ofStabilizer.isMultiplyPretransitive · cited by 2ofStabilizer.isMultiplyPr…AddAction.IsPretransitive.of_vadd_eq · cited by 2IsPretransitive.of_vadd_eqAddAction.IsPretransitive.of_embedding · cited by 1IsPretransitive.of_embedd…HVAdd.hVAdd · cited by 1820HVAdd.hVAddVAdd · cited by 616VAddAddAction.IsPretransitive · cited by 56AddAction.IsPretransitiveIsPretransitive.exists_vadd_eqCITED BYCITES

Cites3

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Cited by6

Results whose statement or proof uses this declaration.