Theorems · Theorem · order theory
le_monotonicSequenceLimit
∀ {α : Type u_1} [inst : PartialOrder α] [WellFoundedGT α] (a : ℕ →o α) (m : ℕ), a m ≤ monotonicSequenceLimit a- Defined in
- Mathlib.Order.OrderIsoNat
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PartialOrderWellFoundedGT
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.
- DFunLike.coestatement · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- LT.lt.leproof · cited by 2,189
- OrderHomstatement and proof · cited by 934
- Eq.geproof · cited by 375
- le_or_gtproof · cited by 269
- WellFoundedGTstatement and proof · cited by 114
- OrderHom.monotoneproof · cited by 70
- Nat.sInf_memproof · cited by 15
- monotonicSequenceLimitstatement · cited by 4
- monotonicSequenceLimitIndexproof · cited by 3
- WellFoundedGT.monotone_chain_conditionproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- WellFoundedGT.iSup_eq_monotonicSequenceLimitproof · cited by 1
- WellFoundedGT.ciSup_eq_monotonicSequenceLimitproof · cited by 0