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Theorems · Theorem · group theory

isUnit_iff_exists_and_exists

∀ {M : Type u_1} [inst : Monoid M] {a : M}, IsUnit a ↔ (∃ b, a * b = 1) ∧ ∃ c, c * a = 1

See isUnit_iff_exists for a similar lemma with one existential.

Defined in
Mathlib.Algebra.Group.Units.Defs
Cited by
1 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
Monoid
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Around this declaration

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

Submodule.ker_unitsToPic · cited by 1Submodule.ker_unitsToPicMonoid · cited by 3887MonoidIsUnit · cited by 1602IsUnitleft_inv_eq_right_inv · cited by 19left_inv_eq_right_invisUnit_iff_exists · cited by 12isUnit_iff_existsisUnit_iff_exists_and_existsCITED BYCITES

Cites4

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Cited by1

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