Theorems · Theorem · order theory
WithTop.mul_top
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : MulZeroClass α] {a : WithTop α}, a ≠ 0 → a * ⊤ = ⊤- Defined in
- Mathlib.Algebra.Order.Ring.WithTop
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext
- Assumes
- DecidableEqMulZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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 and proof · cited by 3,754
- MulZeroClassstatement and proof · cited by 232
- WithTop.mul_top'proof · cited by 3
Cited by9
Results whose statement or proof uses this declaration.
- ENNReal.mul_topproof · cited by 26
- ENat.mul_topproof · cited by 9
- MeromorphicAt.meromorphicTrailingCoeffAt_zpowproof · cited by 5
- meromorphicOrderAt_zpowproof · cited by 4
- WithTop.mul_right_strictMonoproof · cited by 2
- WithTop.untopD_zero_mulproof · cited by 2
- WithTop.mul_lt_mulproof · cited by 1
- WithTop.mul_defproof · cited by 1
- WithTop.coe_mul_eq_bindproof · cited by 0