Finite Field
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Declaration

norm_sq_sub_of_dot_zero

Mathlib.Vector.Dot

Packages

2

Module

63

Theorem

750

Declarations

1016

信頼境界外の sidecar

Source text や表示 overlay は提示用メタデータです。信頼する証拠は署名済み証明書と checker の結果です。

Statement

forall (u : Vec), forall (v : Vec), forall (h : @Eq.{1} RingElem (dot u v) zero), @Eq.{1} RingElem (normSq (vec_sub u v)) (add (normSq u) (normSq v))

Proof term

fun u => fun v => fun h => @Eq.refl.{1} RingElem (normSq (vec_sub u v))

Constants

Mathlib.Algebra.Ring.RingElem

Interface hash: sha256:29d995d6a38e44a010f577d64428b3272226781f7982e2306784cb3bdc4977ea

Mathlib.Algebra.Ring.add

Interface hash: sha256:70894d2717280dc0e45d28bdc4220a44c51506cccc224ab1f339c97d87eedd41

Mathlib.Algebra.Ring.zero

Interface hash: sha256:acd114675ba5b92c602836fd317cdd80e63659c99ff34e05341dda09002571d5

Mathlib.Vector.Basic.Vec

Interface hash: sha256:bc9e713ccaaae78bf5ef428fe3455d47b8f8432e58b79a82bf806866b713e287

Mathlib.Vector.Basic.vec_sub

Interface hash: sha256:2448bcd101acb31d3756f9617d2e06a12117058937c4514c506217480afbccad

Mathlib.Vector.Dot.dot

Interface hash: sha256:98e85b682ad6b2c6a8f2d8865f42ae643087bbcc15c7cfc9ea061cede03ad156

Mathlib.Vector.Dot.normSq

Interface hash: sha256:e89a4cf0ff7a9999826538788b1513030a233e0b0176dc670e9b295817ee48e4

Std.Logic.Eq.Eq

Interface hash: sha256:ca4f8520fd678a809c3ebf0bc7fa38d3063ca4d231e79d567de888685449a015