Theorems · Theorem · ring theory
Commute.sq_sub_sq
∀ {R : Type u} [inst : Ring R] {a b : R}, Commute a b → a ^ 2 - b ^ 2 = (a + b) * (a - b)- Defined in
- Mathlib.Algebra.Ring.Commute
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Commutestatement and proof · cited by 639
- sqproof · cited by 280
- Commute.mul_self_sub_mul_self_eqproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- sq_sub_sqproof · cited by 12
- Commute.sq_eq_sq_iff_eq_or_eq_negproof · cited by 2