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Theorems · Theorem · group theory

Set.smul_set_singleton

∀ {α : Type u_2} {β : Type u_3} [inst : SMul α β] {a : α} {b : β}, a • {b} = {a • b}
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Scalar
Cited by
5 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SMul
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Around this declaration

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

MulAction.stabilizer_singleton · cited by 1MulAction.stabilizer_sing…Ideal.Quotient.smul_top · cited by 1Quotient.smul_topMulAction.IsBlock.singleton · cited by 1IsBlock.singletonSubmodule.smul_one_eq_span · cited by 0Submodule.smul_one_eq_spantotallyDisconnectedSpace_iff_connectedComponent_one · cited by 0totallyDisconnectedSpace_…Set · cited by 53352SetSet.smulSet · cited by 608Set.smulSetSet.image_singleton · cited by 174Set.image_singletonSet.smul_set_singletonCITED BYCITES

Cites3

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Cited by5

Results whose statement or proof uses this declaration.