Theorems · Theorem · order theory

AddLECancellable.mul_tsub

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

Defined in

Mathlib.Algebra.Order.Ring.Canonical

Cited by

1 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext, Quot.sound

Assumes

NonUnitalNonAssocSemiringPartialOrderCanonicallyOrderedAddSubOrderedSubStd.Total