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Theorems · Theorem · group theory

AddLeftCancelMonoid.add_eq_zero

∀ {α : Type u} [inst : AddLeftCancelMonoid α] [Subsingleton (AddUnits α)] {a b : α}, a + b = 0 ↔ a = 0 ∧ b = 0
Defined in
Mathlib.Algebra.Group.Units.Basic
Cited by
4 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext
Assumes
AddLeftCancelMonoidSubsingleton
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Around this declaration

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

FreeAddSemigroup.toFreeAddMonoid_ne_zero · cited by 1FreeAddSemigroup.toFreeAd…AddLeftCancelMonoid.add_ne_zero · cited by 1AddLeftCancelMonoid.add_n…AddSubmonoid.closure_addIrreducible · cited by 0AddSubmonoid.closure_addI…add_eq_zero' · cited by 0add_eq_zero'add_zero · cited by 2707add_zeroAddUnits · cited by 325AddUnitsAddLeftCancelMonoid · cited by 37AddLeftCancelMonoidAddLeftCancelMonoid.eq_zero_of_add_right · cited by 3AddLeftCancelMonoid.eq_ze…AddLeftCancelMonoid.eq_zero_of_add_left · cited by 2AddLeftCancelMonoid.eq_ze…AddLeftCancelMonoid.add_eq_ze…CITED BYCITES

Cites5

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Cited by4

Results whose statement or proof uses this declaration.