StrictAntiOn.slope_neg
∀ {k : Type u_1} {E : Type u_2} [inst : Field k] [inst_1 : AddCommGroup E] [inst_2 : Module k E]
[inst_3 : LinearOrder k] [IsStrictOrderedRing k] [inst_5 : PartialOrder E] [IsOrderedAddMonoid E] [PosSMulMono k E]
{f : k → E} {x y : k} {s : Set k}, StrictAntiOn f s → x ∈ s → y ∈ s → x ≠ y → slope f x y < 0- Defined in
- Mathlib.LinearAlgebra.AffineSpace.Slope
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- PartialOrderstatement and proof · cited by 6,410
- IsStrictOrderedRingstatement and proof · cited by 2,490
- IsOrderedAddMonoidstatement and proof · cited by 1,659
- PosSMulMonostatement and proof · cited by 188
- slopestatement · cited by 147
- StrictAntiOnstatement and proof · cited by 120
- slope_negproof · cited by 10
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