Theorems · Theorem · order theory
irrefl_of
∀ {α : Sort u_1} (r : α → α → Prop) [Std.Irrefl r] (a : α), ¬r a a- Defined in
- Mathlib.Order.Defs.Unbundled
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 4 from the axioms · uses no axioms
- Assumes
- Std.Irrefl
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- irreflproof · cited by 15
Cited by8
Results whose statement or proof uses this declaration.
- ZFSet.mem_irreflproof · cited by 2
- Class.mem_irreflproof · cited by 2
- List.lex_cons_iffproof · cited by 1
- SetRel.irreflproof · cited by 1
- PSet.mem_irreflproof · cited by 1
- injective_of_increasingproof · cited by 1
- Cycle.Chain.eq_nil_of_irreflproof · cited by 1
- Relation.cutExpand_le_invImage_lexproof · cited by 0