Theorems · Theorem · commutative algebra
Submodule.mul_one_div_le_one
∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : CommSemiring A] [inst_2 : Algebra R A]
{I : Submodule R A}, I * (1 / I) ≤ 1- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- mul_commproof · cited by 2,262
- Submodule.mul_leproof · cited by 13
- Submodule.mem_div_iff_forall_mul_memproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.mul_one_div_le_oneproof · cited by 1