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Theorems · Theorem · order theory

Set.projIci_of_le

∀ {α : Type u_1} [inst : LinearOrder α] {a x : α}, x ≤ a → Set.projIci a x = ⟨a, ⋯⟩
Defined in
Mathlib.Order.Interval.Set.ProjIcc
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
LinearOrder
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Around this declaration

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

Set.IciExtend_of_le · cited by 1Set.IciExtend_of_leSet.projIci_self · cited by 0Set.projIci_selfSet · cited by 53352SetLinearOrder · cited by 8572LinearOrderSet.Elem · cited by 7166Set.Elemle_rfl · cited by 1558le_rflSet.Ici · cited by 1070Set.Icimax_eq_left · cited by 96max_eq_leftSet.projIci · cited by 13Set.projIciSet.projIci_of_leCITED BYCITES

Cites7

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.