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Theorems · Theorem · order theory

Set.infinite_of_injective_forall_mem

∀ {α : Type u} {β : Type v} [Infinite α] {s : Set β} {f : α → β},
  Function.Injective f → (∀ (x : α), f x ∈ s) → s.Infinite
Defined in
Mathlib.Data.Set.Finite.Basic
Cited by
2 results in Mathlib
Foundations
Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Infinite
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Around this declaration

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Set.infinite_of_forall_exists_gt · cited by 2Set.infinite_of_forall_ex…Algebraic.infinite_of_charZero · cited by 1Algebraic.infinite_of_cha…Set · cited by 53352SetInfinite · cited by 352InfiniteSet.Infinite · cited by 263Set.InfiniteSet.range_subset_iff · cited by 99Set.range_subset_iffSet.Infinite.mono · cited by 25Infinite.monoSet.infinite_range_of_injective · cited by 9Set.infinite_range_of_inj…Set.infinite_of_injective_for…CITED BYCITES

Cites6

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Cited by2

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