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Mathlib/ModelTheory/PartialTypes.lean

Lines changed: 3 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -224,10 +224,10 @@ theorem partialType_completeTheory_iff_finitelyRealizable
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have hψexM : ψ.exClosure.Realize M :=
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((L.realize_iff_of_model_completeTheory M N ψ.exClosure).1 hψexN)
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obtain ⟨vM, hvM⟩ :=
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Formula.exists_realize_equivSentence_of_realize_exClosure hψexM
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(Formula.exists_realize_equivSentence_iff_realize_exClosure.mpr hψexM)
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have hψM : ψ.Realize vM := by
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letI : (constantsOn α).Structure M := constantsOn.structure vM
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simpa using (Formula.realize_equivSentence M ψ).1 hvM
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simpa [Equiv.symm_apply_apply] using
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(Formula.realize_equivSentence_symm M (Formula.equivSentence ψ) vM).mpr hvM
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exists vM
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aesop
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· intro h

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