Theorems · Theorem · order theory
WithTop.mul_lt_mul
∀ {α : Type u_1} [inst : DecidableEq α] [inst_1 : CommSemiring α] [inst_2 : PartialOrder α] [OrderBot α]
[inst_4 : CanonicallyOrderedAdd α] [PosMulStrictMono α] {a₁ a₂ b₁ b₂ : WithTop α},
a₁ < a₂ → b₁ < b₂ → a₁ * b₁ < a₂ * b₂- Defined in
- Mathlib.Algebra.Order.Ring.WithTop
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Top.topproof · cited by 9,680
- PartialOrderstatement and proof · cited by 6,410
- WithTopstatement and proof · cited by 3,754
- LT.lt.ne'proof · cited by 1,417
- WithTop.someproof · cited by 1,128
- eq_or_neproof · cited by 1,117
- OrderBotstatement and proof · cited by 1,055
- LT.lt.neproof · cited by 872
- CanonicallyOrderedAddstatement and proof · cited by 229
- PosMulStrictMonostatement and proof · cited by 151
- MulPosStrictMonoproof · cited by 94
Cited by1
Results whose statement or proof uses this declaration.
- ENNReal.mul_lt_mulproof · cited by 5