Theorems · Theorem · order theory
WithTop.coe_lt_top
∀ {α : Type u_1} [inst : LT α] (a : α), ↑a < ⊤- Defined in
- Mathlib.Order.WithBot
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
- Assumes
- LT
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- WithTopstatement · cited by 3,754
- WithTop.somestatement · cited by 1,128
- WithTop.coe_injproof · cited by 21
- WithTop.top_ne_coeproof · cited by 15
- WithTop.lt_def'proof · cited by 4
Cited by44
Results whose statement or proof uses this declaration.
- ENNReal.coe_lt_topproof · cited by 52
- EReal.coe_lt_topproof · cited by 17
- WithTop.natCast_lt_topproof · cited by 7
- Dynamics.coverMincard_finite_iffproof · cited by 6
- WithTop.top_posproof · cited by 6
- Polynomial.coeff_eq_zero_of_lt_natTrailingDegreeproof · cited by 5
- Set.finite_of_encard_le_coeproof · cited by 5
- WithTop.strictMono_iffproof · cited by 4
- WithTop.image_coe_Iicproof · cited by 4
- Matrix.IsPivotedBy.eq_top_iffproof · cited by 3
- WithTop.lt_top_iff_ne_topproof · cited by 3
- WithTop.iSup_coe_eq_topproof · cited by 3