Theorems · Theorem · linear algebra
AlternatingMap.constOfIsEmpty_apply
∀ (R : Type u_1) [inst : Semiring R] (M : Type u_2) [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {N : Type u_3}
[inst_3 : AddCommMonoid N] [inst_4 : Module R N] (ι : Type u_7) [inst_5 : IsEmpty ι] (m : N),
⇑(AlternatingMap.constOfIsEmpty R M ι m) = Function.const (ι → M) m- Defined in
- Mathlib.LinearAlgebra.Alternating.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- IsEmptystatement and proof · cited by 759
- AlternatingMapstatement · cited by 329
- AlternatingMap.constOfIsEmptystatement and proof · cited by 13
Cited by8
Results whose statement or proof uses this declaration.
- Orientation.eq_or_eq_neg_of_isEmptyproof · cited by 6
- Orientation.volumeForm_robust'proof · cited by 3
- exteriorPower.zeroEquiv_ιMultiproof · cited by 2
- Orientation.abs_volumeForm_apply_leproof · cited by 2
- Orientation.volumeForm_mapproof · cited by 2
- Orientation.volumeForm_zero_negproof · cited by 1
- Orientation.abs_volumeForm_apply_of_pairwise_orthogonalproof · cited by 1
- Orientation.volumeForm_comp_linearIsometryEquivproof · cited by 0