Theorems · Definition · order theory
RelIso.preimage
{α : Type u_1} → {β : Type u_2} → (f : α ≃ β) → (s : β → β → Prop) → ⇑f ⁻¹'o s ≃r sAny equivalence lifts to a relation isomorphism between s and its preimage.
- Defined in
- Mathlib.Order.RelIso.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 15 from the axioms · 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
- RelIsostatement · cited by 456
- Order.Preimagestatement · cited by 42
Cited by12
Results whose statement or proof uses this declaration.
- Ordinal.lift_id'proof · cited by 10
- Ordinal.lift_addproof · cited by 6
- RelIso.ordinal_lift_type_eqproof · cited by 3
- Ordinal.lift_umaxproof · cited by 2
- Ordinal.lift_type_leproof · cited by 1
- RelIso.preimage_applystatement · cited by 0
- RelIso.preimage_symm_applystatement · cited by 0
- Ordinal.type_lift_preimageproof · cited by 0
- Ordinal.lift_mulproof · cited by 0
- Ordinal.type_preimageproof · cited by 0
- Ordinal.lift_type_eqproof · cited by 0
- Ordinal.lift_type_ltproof · cited by 0