Theorems · Theorem · order theory
IncidenceAlgebra.prod_mul_prod
∀ {𝕜 : Type u_2} {α : Type u_5} {β : Type u_6} [inst : CommRing 𝕜] [inst_1 : Preorder α] [inst_2 : Preorder β]
[inst_3 : LocallyFiniteOrder α] [inst_4 : LocallyFiniteOrder β] [inst_5 : DecidableLE (α × β)]
(f₁ f₂ : IncidenceAlgebra 𝕜 α) (g₁ g₂ : IncidenceAlgebra 𝕜 β), f₁.prod g₁ * f₂.prod g₂ = (f₁ * f₂).prod (g₁ * g₂)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Preorderstatement and proof · cited by 7,952
- LocallyFiniteOrderstatement and proof · cited by 658
- mul_mul_mul_commproof · cited by 65
- IncidenceAlgebrastatement and proof · cited by 51
- IncidenceAlgebra.prodstatement · cited by 7
- IncidenceAlgebra.prod_mul_prod'proof · cited by 2
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