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Theorems · Theorem · order theory

Set.subset_preimage_univ

∀ {α : Type u_1} {β : Type u_2} {f : α → β} {s : Set α}, s ⊆ f ⁻¹' Set.univ
Defined in
Mathlib.Data.Set.Image
Cited by
7 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
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Around this declaration

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

ContMDiff.comp · cited by 15ContMDiff.compContDiffWithinAt.add · cited by 7ContDiffWithinAt.addContDiffWithinAt.smul · cited by 6ContDiffWithinAt.smulContDiffWithinAt.neg · cited by 6ContDiffWithinAt.negHasMFDerivAt.comp · cited by 4HasMFDerivAt.compContMDiff.comp_contMDiffOn · cited by 2ContMDiff.comp_contMDiffOnHasMFDerivAt.comp_hasMFDerivWithinAt · cited by 1HasMFDerivAt.comp_hasMFDe…Set · cited by 53352SetSet.preimage · cited by 4946Set.preimageSet.univ · cited by 3945Set.univSet.subset_univ · cited by 228Set.subset_univSet.subset_preimage_univCITED BYCITES

Cites4

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

Cited by7

Results whose statement or proof uses this declaration.