Theorems · Theorem · order theory
IsChain.lt_of_le
∀ {α : Type u_1} [inst : PartialOrder α] {s : Set α},
IsChain (fun x1 x2 => x1 ≤ x2) s → IsChain (fun x1 x2 => x1 < x2) s- Defined in
- Mathlib.Order.Preorder.Chain
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- IsChainstatement and proof · cited by 158
- Ne.lt_of_leproof · cited by 27
- Ne.lt_of_le'proof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- IsMaxChain.range_fin_of_covByproof · cited by 0
- Flag.chain_ltproof · cited by 0