Theorems · Theorem · linear algebra
Submodule.finrank_lt_finrank_of_lt
∀ {K : Type u} {V : Type v} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
{s t : Submodule K V} [FiniteDimensional K ↥t], s < t → Module.finrank K ↥s < Module.finrank K ↥t- Cited by
- 6 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Submodulestatement and proof · cited by 7,192
- LT.lt.leproof · cited by 2,189
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement · cited by 1,770
- DivisionRingstatement and proof · cited by 1,062
- not_le_of_gtproof · cited by 97
- LinearEquiv.finrank_eqproof · cited by 65
- Eq.trans_ltproof · cited by 34
- Submodule.comapSubtypeEquivOfLeproof · cited by 10
- Submodule.finrank_ltproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- LinearIsometryEquiv.reflections_generate_dim_auxproof · cited by 1
- Submodule.finrank_strictMonoproof · cited by 1
- LieAlgebra.InvariantForm.atomisticproof · cited by 1
- Module.End.exists_ker_pow_eq_ker_pow_succproof · cited by 1
- Module.End.pos_finrank_genEigenspace_of_hasEigenvalueproof · cited by 1
- AffineIndependent.card_lt_card_of_affineSpan_lt_affineSpanproof · cited by 0