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Theorems · Theorem · group theory

addCommute_iff_eq

∀ {S : Type u_3} [inst : Add S] (a b : S), AddCommute a b ↔ a + b = b + a
Defined in
Mathlib.Algebra.Group.Commute.Defs
Cited by
9 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
Add
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Around this declaration

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

Set.addCenter_prod · cited by 3Set.addCenter_prodSet.addCenter_pi · cited by 2Set.addCenter_piNat.addCommute_cast · cited by 2Nat.addCommute_castAddCommute.of_addOrderOf_dvd_two · cited by 1AddCommute.of_addOrderOf_…Set.add_mem_addCenter · cited by 1Set.add_mem_addCenterIsAddLeftRegular.addCommute_add_left_iff · cited by 0IsAddLeftRegular.addCommu…Ordinal.addCommute_iff_eq_mul_natCast · cited by 0Ordinal.addCommute_iff_eq…IsAddRightRegular.addCommute_add_right_iff · cited by 0IsAddRightRegular.addComm…Set.zero_mem_addCenter · cited by 0Set.zero_mem_addCenterAddCommute · cited by 185AddCommuteaddCommute_iff_eqCITED BYCITES

Cites1

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

Cited by9

Results whose statement or proof uses this declaration.