Theorems · Theorem · order theory

mul_self_tsub_mul_self

∀ {R : Type u} [inst : CommSemiring R] [inst_1 : PartialOrder R] [CanonicallyOrderedAdd R] [inst_3 : Sub R]
  [OrderedSub R] [Std.Total fun x1 x2 => x1 ≤ x2] [AddLeftReflectLE R] (a b : R), a * a - b * b = (a + b) * (a - b)

The tsub version of mul_self_sub_mul_self. Notably, this holds for Nat and NNReal.

Defined in

Mathlib.Algebra.Order.Ring.Canonical

Cited by

2 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringPartialOrderCanonicallyOrderedAddSubOrderedSubStd.TotalAddLeftReflectLE