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Theorems · Theorem · order theory

LE.le.trans_ssubset

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

Set notation form of LE.le.trans_lt

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

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

HasSubset.Subset.trans_ssubset · cited by 0Subset.trans_ssubsetMatroid.Indep.ssubset_ground · cited by 0Indep.ssubset_groundPreorder · cited by 7952PreorderLE.le.trans_lt · cited by 795le.trans_ltle.trans_ssubsetCITED BYCITES

Cites2

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.