Theorems · Theorem · order theory
Finsupp.lex_lt_of_lt_of_preorder
∀ {α : Type u_1} {N : Type u_2} [inst : Zero N] [inst_1 : Preorder N] (r : α → α → Prop) [IsStrictOrder α r]
{x y : α →₀ N}, x < y → ∃ i, (∀ (j : α), r j i → x j ≤ y j ∧ y j ≤ x j) ∧ x i < y i- Defined in
- Mathlib.Data.Finsupp.Lex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- ZeroPreorderIsStrictOrder
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Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- Finsuppstatement and proof · cited by 5,255
- IsStrictOrderstatement and proof · cited by 28
- DFinsupp.lex_lt_of_lt_of_preorderproof · cited by 3
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