Theorems · Theorem · order theory
RelIso.rel_symm_apply
∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} (e : r ≃r s) {x : α} {y : β},
r x (e.symm y) ↔ s (e x) y- Defined in
- Mathlib.Order.RelIso.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 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 and proof · cited by 62,936
- RelIsostatement and proof · cited by 456
- RelIso.symmstatement · cited by 193
- RelIso.map_rel_iffproof · cited by 17
- RelIso.apply_symm_applyproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- OrderIso.le_symm_applyproof · cited by 14
- OrderIso.symm_apply_leproof · cited by 5