Theorems · Theorem · order theory
Eq.trans_le
∀ {α : Type u_1} {a b c : α} [inst : LE α], a = b → b ≤ c → a ≤ cAlias of le_of_eq_of_le.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 155 results in Mathlib
- Foundations
- Depth 5 from the axioms, rests on 4 definitions · uses no axioms
- Assumes
- LE
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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 by155
Results whose statement or proof uses this declaration.
- Eq.trans_subsetproof · cited by 16
- AlgebraicGeometry.Scheme.Hom.ker_applyproof · cited by 14
- mul_le_mul_of_nonpos_rightproof · cited by 13
- mul_le_mul_of_nonpos_leftproof · cited by 11
- MeasurableEmbedding.lintegral_mapproof · cited by 10
- IntermediateField.le_normalClosureproof · cited by 8
- cauchy_nhdsproof · cited by 7
- ENNReal.lintegral_mul_le_Lp_mul_Lqproof · cited by 6
- Metric.thickening_of_nonposproof · cited by 6
- AlgebraicGeometry.Proj.basicOpen_monoproof · cited by 5
- AlgebraicGeometry.Scheme.IdealSheafData.map_idealproof · cited by 5
- AlgebraicGeometry.Scheme.Hom.image_preimage_leproof · cited by 5