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Theorems · Theorem · logic and foundations

FirstOrder.Field.realize_eqZero

∀ {K : Type u_1} [inst : CommRing K] [inst_1 : FirstOrder.Ring.CompatibleRing K] (n : ℕ) (v : Empty → K),
  FirstOrder.Language.Formula.Realize (FirstOrder.Field.eqZero n) v ↔ ↑n = 0
Defined in
Mathlib.ModelTheory.Algebra.Field.CharP
Cited by
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Foundations
Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingFirstOrder.Ring.CompatibleRing
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Around this declaration

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DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingmap_natCast · cited by 134map_natCastFirstOrder.Language.Formula.Realize · cited by 81Formula.RealizeFirstOrder.Language.ring · cited by 36Language.ringFirstOrder.Ring.CompatibleRing · cited by 27Ring.CompatibleRingFreeCommRing.lift · cited by 10FreeCommRing.liftFirstOrder.Ring.realize_termOfFreeCommRing · cited by 5Ring.realize_termOfFreeCo…FirstOrder.Ring.realize_zero · cited by 5Ring.realize_zeroFirstOrder.Field.eqZero · cited by 3Field.eqZeroField.realize_eqZeroCITED BYCITES

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