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Theorems · Theorem · order theory

le_self_mul

∀ {α : Type u} [inst : Mul α] [inst_1 : LE α] [CanonicallyOrderedMul α] {a b : α}, a ≤ a * b
Defined in
Mathlib.Algebra.Order.Monoid.Canonical.Defs
Cited by
5 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
MulLECanonicallyOrderedMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

le_iff_exists_mul · cited by 4le_iff_exists_mulself_le_mul_right · cited by 1self_le_mul_rightle_mul_of_le_left · cited by 1le_mul_of_le_leftle_of_mul_le_left · cited by 0le_of_mul_le_leftList.monotone_prod_take · cited by 0List.monotone_prod_takeCanonicallyOrderedMul · cited by 51CanonicallyOrderedMulCanonicallyOrderedMul.le_self_mul · cited by 1CanonicallyOrderedMul.le_…le_self_mulCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.