Theorems · Theorem · commutative algebra
Submodule.set_smul_le_of_le_le
∀ {R : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {S : Type u_4}
[inst_3 : Monoid S] [inst_4 : DistribMulAction S M] {s t : Set S} {p q : Submodule R M}, s ⊆ t → p ≤ q → s • p ≤ t • q- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- Monoidstatement and proof · cited by 3,887
- le_transproof · cited by 985
- DistribMulActionstatement and proof · cited by 584
- Submodule.pointwiseSetSMulstatement · cited by 30
- smul_mono_rightproof · cited by 18
- Submodule.set_smul_mono_leftproof · cited by 3
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