Theorems · Theorem · order theory
RelIso.eq_iff_eq
∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : β → β → Prop} (f : r ≃r s) {a b : α}, f a = f b ↔ a = b- Defined in
- Mathlib.Order.RelIso.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses 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
- RelIsostatement and proof · cited by 456
- RelIso.injectiveproof · cited by 3
Cited by18
Results whose statement or proof uses this declaration.
- Subgroup.op_injproof · cited by 2
- AddSubgroup.op_injproof · cited by 2
- Sym2.fromRel_eq_fromRel_iff_eqproof · cited by 2
- Subsemigroup.op_injproof · cited by 1
- Submonoid.op_injproof · cited by 1
- OrderIso.isAtomic_iffproof · cited by 1
- Subsemiring.op_injproof · cited by 1
- AddSubmonoid.op_injproof · cited by 1
- AddSubsemigroup.op_injproof · cited by 1
- Subring.op_injproof · cited by 1
- Subgroup.unop_injproof · cited by 0
- AddSubgroup.unop_injproof · cited by 0