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Theorems · Theorem · group theory

Set.image_one

∀ {α : Type u_2} {β : Type u_3} [inst : One α] {f : α → β}, f '' 1 = {f 1}
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by
5 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
One
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Around this declaration

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

Set.image_pow · cited by 1Set.image_powSet.preimage_mul_right_one · cited by 1Set.preimage_mul_right_oneMultiplicative.toAdd_image_nsmul · cited by 1Multiplicative.toAdd_imag…Set.preimage_mul_left_one · cited by 1Set.preimage_mul_left_oneIsSemisimpleRing.ideal_eq_span_idempotent · cited by 0IsSemisimpleRing.ideal_eq…Set · cited by 53352SetSet.image · cited by 5609Set.imageSet.image_singleton · cited by 174Set.image_singletonSet.one · cited by 54Set.oneSet.image_oneCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.