Theorems · Theorem · order theory
Prod.mk_lt_mk
∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] {a₁ a₂ : α} {b₁ b₂ : β},
(a₁, b₁) < (a₂, b₂) ↔ a₁ < a₂ ∧ b₁ ≤ b₂ ∨ a₁ ≤ a₂ ∧ b₁ < b₂- Defined in
- Mathlib.Order.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
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
- Prod.lt_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Prod.fst_eq_or_snd_eq_of_wcovByproof · cited by 2
- Submodule.map_strict_mono_or_ker_sup_lt_ker_supproof · cited by 2
- AddMonoidHom.inr_strictMonoproof · cited by 0
- AddMonoidHom.inl_strictMonoproof · cited by 0