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Theorems · Theorem · order theory

UpperSet.sdiff_singleton

∀ {α : Type u_1} [inst : Preorder α] (s : UpperSet α) (a : α), s.sdiff {a} = s.erase a
Defined in
Mathlib.Order.UpperLower.Closure
Cited by
2 results in Mathlib
Foundations
Depth 13 from the axioms · uses propext, Quot.sound
Assumes
Preorder
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Around this declaration

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

UpperSet.erase_inf_Ici · cited by 2UpperSet.erase_inf_IciUpperSet.erase_eq · cited by 1UpperSet.erase_eqSet · cited by 53352SetSetLike.coe · cited by 8199SetLike.coePreorder · cited by 7952PreorderSet.Iic · cited by 1111Set.IicUpperSet · cited by 245UpperSetlowerClosure · cited by 83lowerClosureUpperSet.erase · cited by 9UpperSet.eraseUpperSet.sdiff · cited by 8UpperSet.sdifflowerClosure_singleton · cited by 8lowerClosure_singletonUpperSet.mk.congr_simp · cited by 2mk.congr_simpUpperSet.sdiff_singletonCITED BYCITES

Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.