Theorems · Theorem
Equiv.eq_symm_apply
∀ {α : Sort u_1} {β : Sort u_2} (e : α ≃ β) {x : β} {y : α}, y = e.symm x ↔ e y = x- Defined in
- Mathlib.Logic.Equiv.Defs
- Cited by
- 85 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
Cited by85
Results whose statement or proof uses this declaration.
- LinearEquiv.eq_symm_applyproof · cited by 20
- CategoryTheory.Adjunction.homEquiv_naturality_leftproof · cited by 14
- Equiv.eq_symm_compproof · cited by 10
- AddEquiv.eq_symm_applyproof · cited by 8
- Equiv.comp_symm_eqproof · cited by 8
- MonovaryOn.sum_smul_comp_perm_le_sum_smulproof · cited by 7
- CommRing.Pic.mk_eq_iffproof · cited by 5
- SSet.yonedaEquiv_symm_naturality_leftproof · cited by 4
- Equiv.pointReflection_involutiveproof · cited by 4
- Tropical.trop_eq_iff_eq_untropproof · cited by 3
- AffineEquiv.eq_symm_applyproof · cited by 3
- MulEquiv.eq_symm_applyproof · cited by 3