slope_def_field
∀ {k : Type u_1} [inst : Field k] (f : k → k) (a b : k), slope f a b = (f b - f a) / (b - a)- Defined in
- Mathlib.LinearAlgebra.AffineSpace.Slope
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- VSub.vsubproof · cited by 817
- slopestatement · cited by 147
- div_eq_inv_mulproof · cited by 146
Cited by7
Results whose statement or proof uses this declaration.
- ConvexOn.le_slope_of_hasDerivWithinAt_Ioiproof · cited by 5
- ConvexOn.slope_le_of_hasDerivWithinAt_Iioproof · cited by 5
- image_le_of_liminf_slope_right_lt_deriv_boundary'proof · cited by 4
- Real.deriv_Gamma_natproof · cited by 2
- ConvexOn.isMinOn_of_leftDeriv_nonpos_of_rightDeriv_nonnegproof · cited by 2
- expNegInvGlue.hasDerivAt_polynomial_eval_inv_mulproof · cited by 2
- exists_deriv_eq_slope'proof · cited by 1