Theorems · Theorem · functional analysis
Orientation.volumeForm_zero_pos
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [_i : Fact (Module.finrank ℝ E = 0)],
positiveOrientation.volumeForm = AlternatingMap.constLinearEquivOfIsEmpty 1- Cited by
- 6 results in Mathlib
- Foundations
- Depth 247 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- LinearEquivstatement · cited by 3,317
- Factstatement and proof · cited by 2,726
- Module.finrankstatement and proof · cited by 1,770
- Orientationproof · cited by 360
- AlternatingMapstatement · cited by 329
- OrthonormalBasis.toBasisproof · cited by 102
- Module.Basis.detproof · cited by 73
Cited by6
Results whose statement or proof uses this declaration.
- Orientation.volumeForm_neg_orientationproof · cited by 6
- Orientation.volumeForm_robust'proof · cited by 3
- Orientation.abs_volumeForm_apply_leproof · cited by 2
- Orientation.volumeForm_mapproof · cited by 2
- Orientation.abs_volumeForm_apply_of_pairwise_orthogonalproof · cited by 1
- Orientation.volumeForm_comp_linearIsometryEquivproof · cited by 0