Theorems · Theorem · order theory
LE.le.trans_eq
∀ {α : Type u_1} {a b c : α} [inst : LE α], a ≤ b → b = c → a ≤ cAlias of le_of_le_of_eq.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 328 results in Mathlib
- Foundations
- Depth 4 from the axioms, rests on 3 definitions · uses no axioms
- Assumes
- LE
Around this declaration
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Cites0
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Nothing in Mathlib beyond the foundations.
Cited by328
Results whose statement or proof uses this declaration.
- disjoint_selfproof · cited by 28
- MeasureTheory.Measure.quasiMeasurePreserving_sndproof · cited by 15
- TopologicalSpace.nhds_generateFromproof · cited by 15
- Matroid.ext_indepproof · cited by 15
- Finset.card_image₂_leproof · cited by 13
- Cardinal.mul_eq_selfproof · cited by 13
- MeasureTheory.Measure.quasiMeasurePreserving_fstproof · cited by 12
- Cardinal.mk_realproof · cited by 11
- MeasureTheory.measure_biUnion_finset_leproof · cited by 10
- Topology.IsInducing.isCompact_iffproof · cited by 9
- Matroid.closure_subset_closure_of_subset_closureproof · cited by 9
- LinearMap.mkContinuous₂_norm_leproof · cited by 8
Showing the 200 most cited of 328.