Theorems · Theorem · logic and foundations

FirstOrder.Language.Substructure.closure_withConstants_eq

∀ {L : FirstOrder.Language} {M : Type w} [inst : L.Structure M] {A s : Set M},
  (FirstOrder.Language.Substructure.closure (L.withConstants ↑A)).toFun s =
    ((FirstOrder.Language.Substructure.closure L).toFun (A ∪ s)).withConstants ⋯

Defined in: Mathlib.ModelTheory.Substructures
Cited by: 0 results in Mathlib
Foundations: Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: FirstOrder.Language.Structure

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Setstatement and proof · cited by 53,352
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LE.le.transstatement and proof · cited by 3,151
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FirstOrder.Language.Structurestatement and proof · cited by 775
FirstOrder.Language.Substructurestatement · cited by 242
Set.subset_union_leftstatement and proof · cited by 142
Set.subset_union_rightproof · cited by 123
FirstOrder.Language.withConstantsstatement and proof · cited by 108
LowerAdjoint.toFunstatement and proof · cited by 105

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