Theorems · Theorem · order theory
Monotone.reflect_lt
∀ {α : Type u} {β : Type v} [inst : LinearOrder α] [inst_1 : Preorder β] {f : α → β},
Monotone f → ∀ {a b : α}, f a < f b → a < b- Defined in
- Mathlib.Order.Monotone.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- LinearOrderPreorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Preorderstatement and proof · cited by 7,952
- Monotonestatement and proof · cited by 1,397
- lt_of_not_geproof · cited by 374
- LT.lt.not_geproof · cited by 305
Cited by14
Results whose statement or proof uses this declaration.
- ConditionallyCompleteLinearOrderedField.coe_lt_inducedMap_iffproof · cited by 4
- lt_of_nsmul_lt_nsmul_rightproof · cited by 4
- lt_of_pow_lt_pow_left'proof · cited by 4
- DenseRange.exists_seq_strictMono_tendstoproof · cited by 2
- LeftOrdContinuous.continuousWithinAt_Iicproof · cited by 2
- Nat.nth_lt_of_lt_countproof · cited by 2
- surjOn_Ioo_of_monotone_surjectiveproof · cited by 2
- DenseRange.exists_seq_strictMono_tendsto_of_ltproof · cited by 1
- Set.rangeSplitting_strictMonoproof · cited by 1
- Nat.lt_of_count_lt_countproof · cited by 1
- Monotone.monovaryproof · cited by 1
- EReal.le_iff_signproof · cited by 0