Theorems · Theorem · order theory
ge_antisymm_iff
∀ {α : Type u_1} [inst : PartialOrder α] {a b : α}, a = b ↔ b ≤ a ∧ a ≤ b- Defined in
- Mathlib.Order.Defs.PartialOrder
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- PartialOrder
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
- ge_of_eqproof · cited by 67
- ge_antisymmproof · cited by 51
Cited by8
Results whose statement or proof uses this declaration.
- inf_eq_rightproof · cited by 64
- inf_eq_leftproof · cited by 41
- Ne.not_ge_or_not_leproof · cited by 2
- sdiff_eq_sdiff_iffproof · cited by 1
- superset_antisymm_iffproof · cited by 0
- bihimp_eq_topproof · cited by 0
- MvPowerSeries.gaussNorm_mul_eq_mulproof · cited by 0
- IsTop.isMax_iffproof · cited by 0