Theorems · Theorem · order theory
strictMono_nat_of_lt_succ
∀ {α : Type u} [inst : Preorder α] {f : ℕ → α}, (∀ (n : ℕ), f n < f (n + 1)) → StrictMono f- Defined in
- Mathlib.Order.Monotone.Basic
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses no axioms
- Assumes
- Preorder
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.
- Preorderstatement and proof · cited by 7,952
- StrictMonostatement · cited by 706
- Nat.rel_of_forall_rel_succ_of_ltproof · cited by 1
Cited by21
Results whose statement or proof uses this declaration.
- pow_right_strictMono₀proof · cited by 8
- strictAnti_nat_of_succ_ltproof · cited by 5
- Nat.exists_strictMono'proof · cited by 4
- IsLUB.exists_seq_strictMono_tendsto_of_notMemproof · cited by 4
- nsmul_left_strictMonoproof · cited by 4
- pow_right_strictMono'proof · cited by 3
- Real.strictMono_eulerMascheroniSeqproof · cited by 3
- Filter.extraction_forall_of_frequentlyproof · cited by 2
- exists_orderEmbedding_covby_of_forall_covby_finiteproof · cited by 2
- Set.infinite_of_forall_exists_gtproof · cited by 2
- MeasureTheory.exists_upperCrossingTime_eqproof · cited by 2
- arithGeom_strictMonoproof · cited by 1