Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.lift_card_closure_le

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {s : Set M},
  Cardinal.lift.{u, w} (Cardinal.mk ↥((FirstOrder.Language.Substructure.closure L).toFun s)) ≤
    max Cardinal.aleph0
      (Cardinal.lift.{u, w} (Cardinal.mk ↑s) + Cardinal.lift.{w, u} (Cardinal.mk ((i : ℕ) × L.Functions i)))

Defined in: Mathlib.ModelTheory.Substructures
Cited by: 1 results in Mathlib
Foundations: Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: FirstOrder.Language.Structure

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

Setstatement and proof · cited by 53,352
SetLike.coestatement · cited by 8,199
Set.Elemstatement and proof · cited by 7,166
LE.le.transproof · cited by 3,151
Cardinalstatement and proof · cited by 2,598
le_reflproof · cited by 2,061
FirstOrder.Languagestatement and proof · cited by 1,084
Cardinal.mkstatement and proof · cited by 942
FirstOrder.Language.Structurestatement and proof · cited by 775
Cardinal.liftstatement and proof · cited by 583
Cardinal.aleph0statement and proof · cited by 521
FirstOrder.Language.Substructurestatement · cited by 242

Cited by1

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FirstOrder.Language.exists_elementarySubstructure_card_eqproof · cited by 1