Mathlib Map

Theorems · Theorem · order theory

strictMono_of_le_iff_le

∀ {α : Type u} {β : Type v} [inst : Preorder α] [inst_1 : Preorder β] {f : α → β},
  (∀ (x y : α), x ≤ y ↔ f x ≤ f y) → StrictMono f
Defined in
Mathlib.Order.Monotone.Defs
Cited by
14 results in Mathlib
Foundations
Depth 5 from the axioms · uses no axioms
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

GaloisCoinsertion.strictMono_l · cited by 10GaloisCoinsertion.strictM…GaloisInsertion.strictMono_u · cited by 6GaloisInsertion.strictMon…OrderMonoidIso.strictMono · cited by 3OrderMonoidIso.strictMonoIdeal.exist_integer_multiples_notMem · cited by 1Ideal.exist_integer_multi…IsLocalization.coeSubmodule_strictMono · cited by 1IsLocalization.coeSubmodu…ZFSet.vonNeumann_strictMono · cited by 1ZFSet.vonNeumann_strictMo…Multiset.powerset_strictMono · cited by 1Multiset.powerset_strictM…Int.cast_strictMono · cited by 1Int.cast_strictMonoMvPolynomial.supported_strictMono · cited by 0MvPolynomial.supported_st…OrderAddMonoidIso.strictMono · cited by 0OrderAddMonoidIso.strictM…OrderAddMonoidIso.strictMono_symm · cited by 0OrderAddMonoidIso.strictM…AffineSubspace.mk'_strictMono · cited by 0AffineSubspace.mk'_strict…IsFractionRing.coeSubmodule_strictMono · cited by 0IsFractionRing.coeSubmodu…OrderMonoidIso.strictMono_symm · cited by 0OrderMonoidIso.strictMono…Preorder · cited by 7952PreorderStrictMono · cited by 706StrictMonolt_iff_lt_of_le_iff_le' · cited by 26lt_iff_lt_of_le_iff_le'strictMono_of_le_iff_leCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by14

Results whose statement or proof uses this declaration.