Theorems · Theorem
Equiv.symm_apply_apply
∀ {α : Sort u} {β : Sort v} (e : α ≃ β) (x : α), e.symm (e x) = x- Defined in
- Mathlib.Logic.Equiv.Defs
- Cited by
- 320 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 58 definitions · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Equivstatement and proof · cited by 8,337
- Equiv.symmstatement · cited by 3,681
- Equiv.left_invproof · cited by 59
Cited by323
Results whose statement or proof uses this declaration.
- Matrix.det_transposeproof · cited by 51
- OrderIso.symm_apply_applyproof · cited by 41
- AlgEquiv.symm_apply_applyproof · cited by 36
- RingEquiv.symm_apply_applyproof · cited by 30
- Equiv.symm_comp_selfproof · cited by 28
- Equiv.piCongrLeft'proof · cited by 22
- AddEquiv.symm_apply_applyproof · cited by 19
- Homeomorph.symm_apply_applyproof · cited by 18
- MulEquiv.symm_apply_applyproof · cited by 17
- CategoryTheory.Adjunction.homEquiv_naturality_leftproof · cited by 14
- Finset.sum_equivproof · cited by 14
- Finset.prod_equivproof · cited by 11
Showing the 200 most cited of 323.