Theorems · Theorem · order theory
Order.IsSuccPrelimit.isMin_of_noMax
∀ {α : Type u_1} {a : α} [inst : Preorder α] [inst_1 : SuccOrder α] [IsSuccArchimedean α] [NoMaxOrder α],
Order.IsSuccPrelimit a → IsMin a- Defined in
- Mathlib.Order.SuccPred.Limit
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- le_rflproof · cited by 1,558
- Nat.iterateproof · cited by 740
- Order.succproof · cited by 633
- SuccOrderstatement and proof · cited by 574
- NoMaxOrderstatement and proof · cited by 340
- IsMinstatement · cited by 277
- Order.IsSuccPrelimitstatement and proof · cited by 157
- IsSuccArchimedeanstatement and proof · cited by 88
- Function.iterate_succ_apply'proof · cited by 72
- LE.le.exists_succ_iterateproof · cited by 4
- Order.not_isSuccPrelimit_succproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Order.not_isSuccLimit_of_noMaxproof · cited by 0
- Order.isSuccPrelimit_iff_of_noMaxproof · cited by 0