Theorems · Theorem · order theory
LE.le.trans
∀ {α : Type u_1} [inst : Preorder α] {a b c : α}, a ≤ b → b ≤ c → a ≤ cAlias of le_trans.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 3,151 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
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Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by3,179
Results whose statement or proof uses this declaration.
- le_imp_le_of_le_of_leproof · cited by 576
- abs_of_nonnegproof · cited by 279
- Filter.Tendsto.mono_leftproof · cited by 125
- le_iSup_of_leproof · cited by 79
- Disjoint.monoproof · cited by 69
- disjoint_iff_inf_leproof · cited by 64
- Matroid.Indep.subset_groundproof · cited by 61
- Set.Ioo_subset_Icc_selfproof · cited by 54
- div_le_div₀proof · cited by 53
- GaloisConnection.monotone_uproof · cited by 53
- abs_of_nonposproof · cited by 53
- le_iSup₂_of_leproof · cited by 52
Showing the 200 most cited of 3,179.