Theorems · Theorem · order theory
RelIso.apply_symm_apply
∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} (e : r ≃r s) (x : β), e (e.symm x) = x- Defined in
- Mathlib.Order.RelIso.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- RelIsostatement and proof · cited by 456
- RelIso.symmstatement · cited by 193
- RelIso.toEquivproof · cited by 113
- Equiv.right_invproof · cited by 68
Cited by8
Results whose statement or proof uses this declaration.
- RelIso.rel_symm_applyproof · cited by 2
- SimpleGraph.Subgraph.map_iso_topproof · cited by 1
- RelIso.symm_trans_selfproof · cited by 1
- RelIso.apply_inv_selfproof · cited by 1
- RelIso.self_comp_symmproof · cited by 0
- SimpleGraph.Iso.symm_apply_reachableproof · cited by 0
- SimpleGraph.Iso.toHom_comp_symm_toHomproof · cited by 0
- RelIso.symm_apply_relproof · cited by 0