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Theorems · Theorem · group theory

Units.exists_iff_ne_zero

∀ {G₀ : Type u_3} [inst : GroupWithZero G₀] {p : G₀ → Prop}, (∃ u, p ↑u) ↔ ∃ x, x ≠ 0 ∧ p x
Defined in
Mathlib.Algebra.GroupWithZero.Units.Basic
Cited by
2 results in Mathlib
Foundations
Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupWithZero
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isUnit_iff_ne_zero · cited by 30isUnit_iff_ne_zeroGroupWithZero.isConj_iff₀ · cited by 0GroupWithZero.isConj_iff₀Units · cited by 2804UnitsUnits.val · cited by 1966Units.valGroupWithZero · cited by 691GroupWithZeroUnits.exists_iff_ne_zeroCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.