Theorems · Theorem · order theory
Pi.lt_def
∀ {ι : Type u_1} {π : ι → Type u_4} [inst : (i : ι) → Preorder (π i)] {x y : (i : ι) → π i},
x < y ↔ x ≤ y ∧ ∃ i, x i < y i- Defined in
- Mathlib.Order.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
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
Cited by25
Results whose statement or proof uses this declaration.
- RootPairing.Base.exists_root_eq_sum_intproof · cited by 7
- Fintype.sum_posproof · cited by 3
- DFinsupp.lex_lt_of_lt_of_preorderproof · cited by 3
- RootPairing.Base.pos_or_neg_of_sum_smul_root_memproof · cited by 2
- Pi.lex_lt_of_lt_of_preorderproof · cited by 1
- Fintype.sum_negproof · cited by 1
- RootPairing.Base.not_nonpos_iff_pos_of_sum_mem_range_rootproof · cited by 1
- lt_of_strongLTproof · cited by 1
- Pi.wcovBy_iff_antisymmRelproof · cited by 1
- ContinuousMap.lt_defproof · cited by 0
- NNReal.hasSum_strict_monoproof · cited by 0
- DFinsupp.lt_defproof · cited by 0