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Theorems · Theorem · order theory

le_iff_exists_mul

∀ {α : Type u} [inst : Mul α] [inst_1 : LE α] [CanonicallyOrderedMul α] {a b : α}, a ≤ b ↔ ∃ c, b = a * c
Defined in
Mathlib.Algebra.Order.Monoid.Canonical.Defs
Cited by
4 results in Mathlib
Foundations
Depth 6 from the axioms · uses no axioms
Assumes
MulLECanonicallyOrderedMul
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Finset.HasMulAntidiagonal.mulAntidiagonal.fst_le · cited by 0mulAntidiagonal.fst_lelt_iff_exists_mul · cited by 0lt_iff_exists_mulexists_one_lt_mul_of_lt · cited by 0exists_one_lt_mul_of_ltFinset.HasMulAntidiagonal.mulAntidiagonal.snd_le · cited by 0mulAntidiagonal.snd_leCanonicallyOrderedMul · cited by 51CanonicallyOrderedMulExistsMulOfLE.exists_mul_of_le · cited by 7ExistsMulOfLE.exists_mul_…le_self_mul · cited by 5le_self_mulle_iff_exists_mulCITED BYCITES

Cites3

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

Cited by4

Results whose statement or proof uses this declaration.