Theorems · Theorem · order theory
eq_zero_of_nonpos
∀ {α : Type u_1} {a : α} [inst : PartialOrder α] [inst_1 : Zero α] [IsBotZeroClass α], a ≤ 0 → a = 0Alias of the forward direction of nonpos_iff_eq_zero.
- Defined in
- Mathlib.Algebra.Order.IsBotOne
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PartialOrderstatement and proof · cited by 6,410
- nonpos_iff_eq_zeroproof · cited by 100
- IsBotZeroClassstatement and proof · cited by 71
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.natTrailingDegree_eq_zero_of_constantCoeff_ne_zeroproof · cited by 1
- LE.le.eq_zeroproof · cited by 0