Theorems · Theorem · order theory
Eq.le
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, a = b → a ≤ bAlias of le_of_eq.
- Defined in
- Mathlib.Order.Basic
- Cited by
- 605 results in Mathlib
- Foundations
- Depth 6 from the axioms, rests on 8 definitions · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by605
Results whose statement or proof uses this declaration.
- Eq.subsetproof · cited by 124
- LE.le.ge_iff_eq'proof · cited by 50
- MeasureTheory.dominatedFinMeasAdditive_weightedSMulproof · cited by 35
- norm_sum_leproof · cited by 25
- Polynomial.eq_C_of_natDegree_eq_zeroproof · cited by 22
- disjoint_sdiff_self_rightproof · cited by 22
- Isometry.lipschitzproof · cited by 22
- disjoint_sdiff_self_leftproof · cited by 21
- Inseparable.specializesproof · cited by 16
- Finpartition.leproof · cited by 15
- MeasureTheory.dominatedFinMeasAdditive_condExpIndproof · cited by 14
- Order.succ_eq_iff_isMaxproof · cited by 11
Showing the 200 most cited of 605.