Mathlib Map

Theorems · Theorem

nonempty_fun

∀ {α : Sort u_1} {β : Sort u_2}, Nonempty (α → β) ↔ IsEmpty α ∨ Nonempty β
Defined in
Mathlib.Logic.IsEmpty.Basic
Cited by
1 results in Mathlib
Foundations
Depth 16 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.

Function.exists_surjective_iff · cited by 0Function.exists_surjectiv…IsEmpty · cited by 759IsEmptynot_iff_not · cited by 159not_iff_notnot_nonempty_iff · cited by 20not_nonempty_iffnot_isEmpty_iff · cited by 19not_isEmpty_iffisEmpty_fun · cited by 1isEmpty_funnonempty_funCITED BYCITES

Cites5

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

Cited by1

Results whose statement or proof uses this declaration.