Orientation.areaForm_to_volumeForm
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : InnerProductSpace ℝ E] [inst_2 : Fact (Module.finrank ℝ E = 2)]
(o : Orientation ℝ E (Fin 2)) (x y : E), (o.areaForm x) y = o.volumeForm ![x, y]- Cited by
- 8 results in Mathlib
- Foundations
- Depth 251 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- LinearMapstatement · cited by 10,215
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- Module.finrankstatement and proof · cited by 1,770
- LinearMap.compproof · cited by 1,642
- LinearEquiv.symmproof · cited by 1,461
- LinearEquiv.toLinearMapproof · cited by 1,171
- Matrix.vecConsstatement and proof · cited by 852
Cited by8
Results whose statement or proof uses this declaration.
- Orientation.areaForm_apply_selfproof · cited by 5
- Orientation.areaForm_swapproof · cited by 5
- Orientation.areaForm_mapproof · cited by 4
- Complex.areaFormproof · cited by 3
- Orientation.areaForm_neg_orientationproof · cited by 2
- Orientation.areaForm_leproof · cited by 0
- Orientation.abs_areaForm_leproof · cited by 0
- Orientation.abs_areaForm_of_orthogonalproof · cited by 0