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Theorems · Theorem · order theory

Prod.lt_iff

∀ {α : Type u_2} {β : Type u_3} [inst : Preorder α] [inst_1 : Preorder β] {x y : α × β},
  x < y ↔ x.1 < y.1 ∧ x.2 ≤ y.2 ∨ x.1 ≤ y.1 ∧ x.2 < y.2
Defined in
Mathlib.Order.Basic
Cited by
2 results in Mathlib
Foundations
Depth 12 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderPreorder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Prod.mk_lt_mk · cited by 4Prod.mk_lt_mkSSet.prodStdSimplex.strictMono_orderHomOfSimplex_iff · cited by 0prodStdSimplex.strictMono…Preorder · cited by 7952PreorderLT.lt.le · cited by 2189lt.leLT.lt.not_ge · cited by 305lt.not_geLE.le.lt_of_not_ge · cited by 21le.lt_of_not_geProd.lt_iffCITED BYCITES

Cites4

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Cited by2

Results whose statement or proof uses this declaration.