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声明
dist_sq_points_def_from_args
Mathlib.Geometry.Affine.Derived
包
2
模块
63
定理
750
声明
1016
非可信 sidecar
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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 (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), forall (affine_args : @AffineLawArgs.{p,u,v} Scalar zero one add neg sub mul le_rel Vector vzero vadd vneg smul inner PointCarrier disp_op), forall (A : PointCarrier), forall (B : PointCarrier), @Eq.{u} Scalar (@distSqPoints.{p,u,v} Scalar Vector inner PointCarrier disp_op A B) (@normSq.{u,v} Scalar Vector inner (@disp.{p,v} PointCarrier Vector disp_op A B))
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 => fun affine_args => fun A => fun B => @Eq.refl.{u} Scalar (@distSqPoints.{p,u,v} Scalar Vector inner PointCarrier disp_op A B)
常量
Mathlib.Geometry.Affine.AffineLawArgs
Interface hash: sha256:5784cd602124756681dcc1321cbc9250895d42148da52ee028142c4fa9fcfd17
Mathlib.Geometry.Affine.disp
Interface hash: sha256:0cb7627a80270a6e2d271580406e4ff4a0dac01affd7c53104ccb02f5471b1e7
Mathlib.Geometry.Affine.distSqPoints
Interface hash: sha256:152d4713ed75cf7a6ba0207cd93a8386aeb981232922aa806b3e33704c0aec91
Mathlib.LinearAlgebra.InnerProduct.normSq
Interface hash: sha256:7deaed46931ec95104c267813d7a6d08bcbd8862a9ff3343231aed7fdab60b04
Std.Logic.Eq.Eq
Interface hash: sha256:ca4f8520fd678a809c3ebf0bc7fa38d3063ca4d231e79d567de888685449a015