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Theorems · Theorem · logic and foundations

PFun.preimage_eq

∀ {α : Type u_1} {β : Type u_2} (f : α →. β) (s : Set β), f.preimage s = f.core s ∩ f.Dom
Defined in
Mathlib.Data.PFun
Cited by
2 results in Mathlib
Foundations
Depth 9 from the axioms · uses propext, Quot.sound
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Around this declaration

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

PFun.core_eq · cited by 0PFun.core_eqFilter.ptendsto'_of_ptendsto · cited by 0Filter.ptendsto'_of_ptend…Set · cited by 53352SetPFun · cited by 207PFunPart.get · cited by 77Part.getSet.subset_inter · cited by 74Set.subset_interPFun.Dom · cited by 28PFun.DomPFun.preimage · cited by 18PFun.preimagePFun.core · cited by 16PFun.coreSet.eq_of_subset_of_subset · cited by 11Set.eq_of_subset_of_subsetPart.get_mem · cited by 6Part.get_memPFun.preimage_subset_core · cited by 2PFun.preimage_subset_corePFun.preimage_subset_dom · cited by 1PFun.preimage_subset_domPFun.preimage_eqCITED BYCITES

Cites11

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

Cited by2

Results whose statement or proof uses this declaration.