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声明

derivative_unique_from_args

Mathlib.Analysis.Calculus.Derivative

2

模块

63

定理

750

声明

1016

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陈述

forall (Scalar : Sort u), forall (zero : Scalar), forall (one : Scalar), forall (add : forall (a : Scalar), forall (b : Scalar), Scalar), forall (neg : forall (a : Scalar), Scalar), forall (sub : forall (a : Scalar), forall (b : Scalar), Scalar), forall (mul : forall (a : Scalar), forall (b : Scalar), Scalar), forall (le_rel : forall (a : Scalar), forall (b : Scalar), Prop), forall (X : Sort v), forall (xzero : X), forall (xadd : forall (x : X), forall (y : X), X), forall (xneg : forall (x : X), X), forall (xsmul : forall (a : Scalar), forall (x : X), X), forall (xnorm : forall (x : X), Scalar), forall (Y : Sort w), forall (yzero : Y), forall (yadd : forall (x : Y), forall (y : Y), Y), forall (yneg : forall (y : Y), Y), forall (ysmul : forall (a : Scalar), forall (y : Y), Y), forall (ynorm : forall (y : Y), Scalar), forall (f : forall (x : X), Y), forall (point : X), forall (unique_args : @DerivativeUniqueArgs.{u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm f point), forall (df_left : forall (h : X), Y), forall (bound_left : Scalar), forall (remainder_left : forall (r : Y), Prop), forall (df_right : forall (h : X), Y), forall (bound_right : Scalar), forall (remainder_right : forall (r : Y), Prop), forall (left_at : @FrechetDerivativeAt.{u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm f point df_left bound_left remainder_left), forall (right_at : @FrechetDerivativeAt.{u,v,w} Scalar zero one add neg sub mul le_rel X xzero xadd xneg xsmul xnorm Y yzero yadd yneg ysmul ynorm f point df_right bound_right remainder_right), forall (h : X), @Eq.{w} Y (df_left h) (df_right h)

证明项

fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun le_rel => fun X => fun xzero => fun xadd => fun xneg => fun xsmul => fun xnorm => fun Y => fun yzero => fun yadd => fun yneg => fun ysmul => fun ynorm => fun f => fun point => fun unique_args => fun df_left => fun bound_left => fun remainder_left => fun df_right => fun bound_right => fun remainder_right => fun left_at => fun right_at => fun h => unique_args df_left bound_left remainder_left df_right bound_right remainder_right left_at right_at h

常量