Theorems · Theorem · commutative algebra
Submodule.length_le_length_restrictScalars
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (A : Type u_5)
[inst_3 : Ring A] [inst_4 : SMul A R] [inst_5 : Module A M] [inst_6 : IsScalarTower A R M] (p : Submodule R M),
Module.length R ↥p ≤ Module.length A ↥(Submodule.restrictScalars A p)- Defined in
- Mathlib.RingTheory.Length
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- ENatstatement and proof · cited by 4,985
- IsScalarTowerstatement and proof · cited by 3,896
- WithBotproof · cited by 1,498
- WithBot.someproof · cited by 541
- Submodule.restrictScalarsstatement and proof · cited by 180
- Order.krullDimproof · cited by 82
- WithBot.coe_le_coeproof · cited by 76
- Module.lengthstatement and proof · cited by 56
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