Theorems · Theorem · order theory
IsLeast.insert
∀ {γ : Type u_3} [inst : LinearOrder γ] (a : γ) {b : γ} {s : Set γ}, IsLeast s b → IsLeast (insert a s) (min a b)- Defined in
- Mathlib.Order.Bounds.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- LinearOrderstatement and proof · cited by 8,572
- IsLeaststatement and proof · cited by 122
- Set.insert_eqproof · cited by 47
- isLeast_singletonproof · cited by 5
- IsLeast.unionproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Finset.min'_insertproof · cited by 1
- isLeast_pairproof · cited by 0