Theorems · Theorem · order theory

AddLECancellable.tsub_mul

∀ {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] [MulRightMono R] {a b c : R},
  AddLECancellable (b * c) → (a - b) * c = a * c - b * c

Defined in

Mathlib.Algebra.Order.Ring.Canonical

Cited by

2 results in Mathlib

Foundations

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

Assumes

NonUnitalNonAssocSemiringPartialOrderCanonicallyOrderedAddSubOrderedSubStd.TotalMulRightMono