Theorems · Theorem · logic and foundations
FirstOrder.Language.Theory.CompleteType.formula_mem_typeOf
∀ {L : FirstOrder.Language} {T : L.Theory} {α : Type w} {M : Type w'} [inst : L.Structure M] [inst_1 : Nonempty M]
[inst_2 : M ⊨ T] {v : α → M} {φ : L.Formula α}, FirstOrder.Language.Formula.equivSentence φ ∈ T.typeOf v ↔ φ.Realize v- Defined in
- Mathlib.ModelTheory.Types
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- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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- FirstOrder.Language.Formula.Realizestatement and proof · cited by 81
- FirstOrder.Language.Theory.Modelstatement and proof · cited by 67
- FirstOrder.Language.Theory.CompleteTypestatement · cited by 35
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