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Theorems · Theorem · group theory

Set.image_zero

∀ {α : Type u_2} {β : Type u_3} [inst : Zero α] {f : α → β}, f '' 0 = {f 0}
Defined in
Mathlib.Algebra.Group.Pointwise.Set.Basic
Cited by
4 results in Mathlib
Foundations
Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Zero
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Around this declaration

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

Set.preimage_add_right_zero · cited by 1Set.preimage_add_right_ze…Set.image_nsmul · cited by 1Set.image_nsmulSet.preimage_add_left_zero · cited by 1Set.preimage_add_left_zeroMultiplicative.ofAdd_image_nsmul · cited by 0Multiplicative.ofAdd_imag…Set · cited by 53352SetSet.image · cited by 5609Set.imageSet.image_singleton · cited by 174Set.image_singletonSet.zero · cited by 87Set.zeroSet.image_zeroCITED BYCITES

Cites4

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Cited by4

Results whose statement or proof uses this declaration.