Theorems · Theorem · linear algebra
rank_top
∀ (R : Type u) (M : Type v) [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M], Module.rank R ↥⊤ = Module.rank R M
- Defined in
- Mathlib.LinearAlgebra.Dimension.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- Cardinalstatement · cited by 2,598
- Module.rankstatement · cited by 496
- LinearEquiv.rank_eqproof · cited by 31
- LinearEquiv.ofTopproof · cited by 14
Cited by9
Results whose statement or proof uses this declaration.
- finrank_topproof · cited by 31
- Submodule.rank_leproof · cited by 5
- rank_range_of_surjectiveproof · cited by 4
- rank_le_one_iffproof · cited by 2
- IntermediateField.rank_top'proof · cited by 2
- Module.rank_le_one_iff_top_isPrincipalproof · cited by 1
- RCLike.rank_le_twoproof · cited by 1
- Ideal.rank_prime_pow_ramificationIdxproof · cited by 1
- Subalgebra.rank_topproof · cited by 1