Mathlib Map

Theorems · Theorem · logic and foundations

Set.encard_pos

∀ {α : Type u_1} {s : Set α}, 0 < s.encard ↔ s.Nonempty
Defined in
Mathlib.Data.Set.Card
Cited by
2 results in Mathlib
Foundations
Depth 94 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.

Set.encard_ne_zero_of_mem · cited by 1Set.encard_ne_zero_of_memSet.Nonempty.encard_pos · cited by 0Nonempty.encard_posSet · cited by 53352SetENat · cited by 4985ENatSet.Nonempty · cited by 2627Set.NonemptySet.encard · cited by 327Set.encardpos_iff_ne_zero · cited by 180pos_iff_ne_zeroSet.encard_ne_zero · cited by 1Set.encard_ne_zeroSet.encard_posCITED BYCITES

Cites6

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.