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Theorems · Theorem · group theory

isAddCommutative_iff

∀ {M : Type u_2} [inst : Add M], IsAddCommutative M ↔ ∀ (a b : M), a + b = b + a
Defined in
Mathlib.Algebra.Group.Defs
Cited by
3 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Add
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Around this declaration

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

AddSubgroup.center_eq_top_iff · cited by 3AddSubgroup.center_eq_top…isAddCommutative_iff_of_setLike · cited by 2isAddCommutative_iff_of_s…IsAddCommutative.of_comm · cited by 0IsAddCommutative.of_commIsAddCommutative · cited by 40IsAddCommutativeisAddCommutative_iffCITED BYCITES

Cites1

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Cited by3

Results whose statement or proof uses this declaration.