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Theorems · Theorem · group theory

IsAddLeftRegular.all

∀ {R : Type u_2} [inst : Add R] [IsLeftCancelAdd R] (g : R), IsAddLeftRegular g

If all additions cancel on the left then every element is add-left-regular.

Defined in
Mathlib.Algebra.Group.Defs
Cited by
5 results in Mathlib
Foundations
Depth 9 from the axioms · uses no axioms
Assumes
AddIsLeftCancelAdd
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Around this declaration

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

WithTop.add_left_inj · cited by 2WithTop.add_left_injAddMonoidAlgebra.support_coeff_single_mul · cited by 1AddMonoidAlgebra.support_…ENat.WithBot.natCast_add_cancel · cited by 1WithBot.natCast_add_cancelENat.WithBot.one_add_cancel · cited by 0WithBot.one_add_cancelIsAddRegular.all · cited by 0IsAddRegular.allIsLeftCancelAdd · cited by 72IsLeftCancelAddIsAddLeftRegular · cited by 58IsAddLeftRegularisLeftCancelAdd_iff · cited by 2isLeftCancelAdd_iffIsAddLeftRegular.allCITED BYCITES

Cites3

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

Cited by5

Results whose statement or proof uses this declaration.