Theorems · Theorem · ring theory
Commute.mul_self_sub_mul_self_eq
∀ {R : Type u} [inst : NonUnitalNonAssocRing R] {a b : R}, Commute a b → a * a - b * b = (a + b) * (a - b)Representation of a difference of two squares of commuting elements as a product.
- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses no axioms
- Assumes
- NonUnitalNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Commutestatement and proof · cited by 639
- add_mulproof · cited by 363
- NonUnitalNonAssocRingstatement and proof · cited by 354
- mul_subproof · cited by 201
- Commute.eqproof · cited by 91
- sub_add_sub_cancelproof · cited by 56
Cited by4
Results whose statement or proof uses this declaration.
- Commute.sq_sub_sqproof · cited by 2
- Commute.mul_self_eq_mul_self_iffproof · cited by 2
- mul_self_sub_mul_selfproof · cited by 0
- mul_self_sub_oneproof · cited by 0