Theorems · Theorem · logic and foundations
FirstOrder.Language.ElementaryEmbedding.map_sentence
∀ {L : FirstOrder.Language} {M : Type u_1} {N : Type u_2} [inst : L.Structure M] [inst_1 : L.Structure N]
(f : L.ElementaryEmbedding M N) (φ : L.Sentence), M ⊨ φ ↔ N ⊨ φ- Defined in
- Mathlib.ModelTheory.ElementaryMaps
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- FirstOrder.Languagestatement and proof · cited by 1,084
- FirstOrder.Language.Structurestatement and proof · cited by 775
- FirstOrder.Language.Sentencestatement and proof · cited by 127
- FirstOrder.Language.Formula.Realizeproof · cited by 81
- FirstOrder.Language.Sentence.Realizestatement and proof · cited by 62
- Unique.eq_defaultproof · cited by 38
- FirstOrder.Language.ElementaryEmbeddingstatement and proof · cited by 33
- FirstOrder.Language.ElementaryEmbedding.map_formulaproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- FirstOrder.Language.ElementaryEmbedding.elementarilyEquivalentproof · cited by 2
- FirstOrder.Language.ElementaryEmbedding.theory_model_iffproof · cited by 1
- FirstOrder.Language.ElementarySubstructure.realize_sentenceproof · cited by 0