slope_neg
∀ {k : Type u_1} {E : Type u_2} [inst : Field k] [inst_1 : AddCommGroup E] [inst_2 : Module k E] (f : k → E) (x y : k),
slope (fun t => -f t) x y = -slope f x y- Defined in
- Mathlib.LinearAlgebra.AffineSpace.Slope
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- neg_subproof · cited by 272
- slopestatement · cited by 147
- neg_sub_negproof · cited by 13
Cited by10
Results whose statement or proof uses this declaration.
- slope_neg_funproof · cited by 3
- ConcaveOn.le_slope_of_hasDerivWithinAt_Iioproof · cited by 3
- ConcaveOn.slope_le_of_hasDerivWithinAt_Ioiproof · cited by 3
- StrictConcaveOn.lt_slope_of_hasDerivWithinAt_Iioproof · cited by 2
- StrictConcaveOn.lt_slope_of_hasDerivWithinAtproof · cited by 1
- StrictConcaveOn.slope_lt_of_hasDerivAtproof · cited by 1
- StrictConcaveOn.slope_lt_of_hasDerivWithinAtproof · cited by 1
- StrictConcaveOn.slope_lt_of_hasDerivWithinAt_Ioiproof · cited by 1
- AntitoneOn.slope_nonposproof · cited by 0
- StrictAntiOn.slope_negproof · cited by 0