Cardinal.infinite_pigeonhole_card

∀ {β α : Type u} (f : β → α),
  ∀ θ ≤ Cardinal.mk β, Cardinal.aleph0 ≤ θ → Cardinal.mk α < θ.ord.cof → ∃ a, θ ≤ Cardinal.mk ↑(f ⁻¹' {a})

Pigeonhole principle for a cardinality below the cardinality of the domain

Defined in: Mathlib.SetTheory.Cardinal.Pigeonhole
Cited by: 4 results in Mathlib
Foundations: Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

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