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Theorems · Theorem · geometry

slope_neg_fun

∀ {k : Type u_1} {E : Type u_2} [inst : Field k] [inst_1 : AddCommGroup E] [inst_2 : Module k E] (f : k → E),
  slope (-f) = -slope f
Defined in
Mathlib.LinearAlgebra.AffineSpace.Slope
Cited by
3 results in Mathlib
Foundations
Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldAddCommGroupModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ConcaveOn.slope_anti · cited by 2ConcaveOn.slope_antislope_neg_iff_of_le · cited by 0slope_neg_iff_of_leslope_nonpos_iff_of_le · cited by 0slope_nonpos_iff_of_leModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupField · cited by 7404Fieldslope · cited by 147slopeslope_neg · cited by 10slope_negslope_neg_funCITED BYCITES

Cites5

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
  • slopestatement · cited by 147
  • slope_negproof · cited by 10

Cited by3

Results whose statement or proof uses this declaration.