Theorems · Theorem · linear algebra
rank_ulift
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M],
Module.rank R (ULift.{w, v} M) = Cardinal.lift.{w, v} (Module.rank R M)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 89 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.
Cites11
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
- Cardinalstatement · cited by 2,598
- LinearEquiv.symmproof · cited by 1,461
- Cardinal.liftstatement and proof · cited by 583
- Module.rankstatement and proof · cited by 496
- Cardinal.lift_liftproof · cited by 53
- ULift.moduleEquivproof · cited by 18
- LinearEquiv.lift_rank_eqproof · cited by 14
- Cardinal.lift_injectiveproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- finrank_uliftproof · cited by 1
- lift_rank_add_lift_rank_le_rank_prodproof · cited by 0