Theorems · Theorem · order theory
smul_min_of_nonneg
∀ {α : Type u_1} {β : Type u_2} {a : α} [inst : SMul α β] [inst_1 : Preorder α] [inst_2 : LinearOrder β]
[inst_3 : Zero α] [PosSMulMono α β], 0 ≤ a → ∀ (b₁ b₂ : β), a • min b₁ b₂ = min (a • b₁) (a • b₂)- Defined in
- Mathlib.Algebra.Order.Module.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
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- LinearOrderstatement and proof · cited by 8,572
- Preorderstatement and proof · cited by 7,952
- PosSMulMonostatement and proof · cited by 188
- Monotone.map_minproof · cited by 43
- monotone_smul_left_of_nonnegproof · cited by 9
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