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Theorems · Theorem · combinatorics

Finset.map_nonempty

∀ {α : Type u_1} {β : Type u_2} {f : α ↪ β} {s : Finset α}, (Finset.map f s).Nonempty ↔ s.Nonempty
Defined in
Mathlib.Data.Finset.Image
Cited by
8 results in Mathlib
Foundations
Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Finset.Nonempty.map · cited by 4Nonempty.mapFinset.sup'_map · cited by 2Finset.sup'_mapFinset.inf'_map · cited by 2Finset.inf'_mapFinset.compls_nonempty · cited by 2Finset.compls_nonemptyFinset.map_truncatedInf · cited by 1Finset.map_truncatedInfFinset.map_truncatedSup · cited by 1Finset.map_truncatedSupFinset.sup'_comp_eq_map · cited by 0Finset.sup'_comp_eq_mapFinset.inf'_comp_eq_map · cited by 0Finset.inf'_comp_eq_mapFinset · cited by 13712FinsetSet.Nonempty · cited by 2627Set.NonemptyFinset.Nonempty · cited by 1001Finset.NonemptyFunction.Embedding · cited by 988Function.EmbeddingFinset.map · cited by 747Finset.mapSet.image_nonempty · cited by 29Set.image_nonemptyFinset.map_nonemptyCITED BYCITES

Cites6

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

Cited by8

Results whose statement or proof uses this declaration.