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声明

AffineLawArgs

Mathlib.Geometry.Affine

2

模块

63

定理

750

声明

1016

非可信 sidecar

源文本和展示 overlay 属于展示元数据。可信证据是签名证书和 checker 结果。

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 (Vector : Sort v), forall (vzero : Vector), forall (vadd : forall (x : Vector), forall (y : Vector), Vector), forall (vneg : forall (x : Vector), Vector), forall (smul : forall (a : Scalar), forall (x : Vector), Vector), forall (inner : forall (x : Vector), forall (y : Vector), Scalar), forall (PointCarrier : Sort p), forall (disp_op : forall (A : PointCarrier), forall (B : PointCarrier), Vector), Prop

证明项

fun Scalar => fun zero => fun one => fun add => fun neg => fun sub => fun mul => fun le_rel => fun Vector => fun vzero => fun vadd => fun vneg => fun smul => fun inner => fun PointCarrier => fun disp_op => forall (P : Prop), forall (mk : forall (disp_self_law : forall (A : PointCarrier), @Eq.{v} Vector (@disp.{p,v} PointCarrier Vector disp_op A A) vzero), forall (disp_reverse_law : forall (A : PointCarrier), forall (B : PointCarrier), @Eq.{v} Vector (@disp.{p,v} PointCarrier Vector disp_op B A) (vneg (@disp.{p,v} PointCarrier Vector disp_op A B))), forall (disp_comp_law : forall (A : PointCarrier), forall (B : PointCarrier), forall (C : PointCarrier), @Eq.{v} Vector (@disp.{p,v} PointCarrier Vector disp_op A C) (vadd (@disp.{p,v} PointCarrier Vector disp_op A B) (@disp.{p,v} PointCarrier Vector disp_op B C))), forall (point_ext_of_zero_disp_law : forall (A : PointCarrier), forall (B : PointCarrier), forall (h : @Eq.{v} Vector (@disp.{p,v} PointCarrier Vector disp_op A B) vzero), @Eq.{p} PointCarrier A B), forall (dist_sq_symm_law : forall (A : PointCarrier), forall (B : PointCarrier), @Eq.{u} Scalar (@distSqPoints.{p,u,v} Scalar Vector inner PointCarrier disp_op A B) (@distSqPoints.{p,u,v} Scalar Vector inner PointCarrier disp_op B A)), forall (dist_sq_zero_iff_eq_law : forall (A : PointCarrier), forall (B : PointCarrier), forall (R : Prop), forall (mk : forall (forward : forall (h : @Eq.{u} Scalar (@distSqPoints.{p,u,v} Scalar Vector inner PointCarrier disp_op A B) zero), @Eq.{p} PointCarrier A B), forall (backward : forall (h : @Eq.{p} PointCarrier A B), @Eq.{u} Scalar (@distSqPoints.{p,u,v} Scalar Vector inner PointCarrier disp_op A B) zero), R), R), P), P