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Theorems · Theorem · logic and foundations

FirstOrder.Language.Equiv.self_comp_symm

∀ {L : FirstOrder.Language} {M : Type w} {N : Type w'} [inst : L.Structure M] [inst_1 : L.Structure N]
  (f : L.Equiv M N), f.comp f.symm = FirstOrder.Language.Equiv.refl L N
Defined in
Mathlib.ModelTheory.Basic
Cited by
3 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FirstOrder.Language.StructureFirstOrder.Language.Structure
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FirstOrder.Language.Equiv.comp_right_injective · cited by 1Equiv.comp_right_injectiveFirstOrder.Language.Equiv.self_comp_symm_toEmbedding · cited by 0Equiv.self_comp_symm_toEm…FirstOrder.Language.Equiv.self_comp_symm_toHom · cited by 0Equiv.self_comp_symm_toHomDFunLike.coe · cited by 62936DFunLike.coeFirstOrder.Language · cited by 1084FirstOrder.LanguageFirstOrder.Language.Structure · cited by 775Language.StructureFirstOrder.Language.Equiv · cited by 83Language.EquivFirstOrder.Language.Equiv.symm · cited by 32Equiv.symmFirstOrder.Language.Equiv.comp · cited by 12Equiv.compFirstOrder.Language.Equiv.refl · cited by 7Equiv.reflFirstOrder.Language.Equiv.apply_symm_apply · cited by 6Equiv.apply_symm_applyFirstOrder.Language.Equiv.ext · cited by 4Equiv.extFirstOrder.Language.Equiv.refl_apply · cited by 2Equiv.refl_applyFirstOrder.Language.Equiv.comp_apply · cited by 2Equiv.comp_applyEquiv.self_comp_symmCITED BYCITES

Cites11

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Cited by3

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