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Theorems · Theorem · order theory

ssubset_of_ne_of_subset

∀ {α : Type u_1} [UsesSetNotationForOrder α] [inst : PartialOrder α] {a b : α}, a ≠ b → a ⊆ b → a ⊂ b

Set notation form of lt_of_ne_of_le

Defined in
Mathlib.Order.RelClasses
Cited by
3 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
UsesSetNotationForOrderPartialOrder
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Around this declaration

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

Set.Finite.induction_to · cited by 1Finite.induction_toSimpleGraph.IsMaximumClique.isMaximalClique · cited by 1IsMaximumClique.isMaximal…Matroid.IsCircuit.contractElem_isCircuit · cited by 0IsCircuit.contractElem_is…PartialOrder · cited by 6410PartialOrderlt_of_ne_of_le · cited by 1lt_of_ne_of_lessubset_of_ne_of_subsetCITED BYCITES

Cites2

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Cited by3

Results whose statement or proof uses this declaration.