perp_iff_dot_eq_zero

Mathlib.Geometry.RightTriangle

Packages

Module

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 (P : Prop), forall (mk : forall (forward : forall (h : Perp u v), @Eq.{1} RingElem (dot u v) zero), forall (backward : forall (h : @Eq.{1} RingElem (dot u v) zero), Perp u v), P), P

Proof term

fun u => fun v => fun P => fun mk => mk (fun (h : Perp u v) => h) (fun (h : @Eq.{1} RingElem (dot u v) zero) => h)

Constants

Mathlib.Algebra.Ring.RingElem

Interface hash: sha256:29d995d6a38e44a010f577d64428b3272226781f7982e2306784cb3bdc4977ea

Mathlib.Algebra.Ring.zero

Interface hash: sha256:acd114675ba5b92c602836fd317cdd80e63659c99ff34e05341dda09002571d5

Mathlib.Geometry.RightTriangle.Perp

Interface hash: sha256:084f8727702314dc0bc3eac7b9d6661d579ea3a57023b15d767a9e98ee4beb79

Mathlib.Vector.Basic.Vec

Interface hash: sha256:bc9e713ccaaae78bf5ef428fe3455d47b8f8432e58b79a82bf806866b713e287

Mathlib.Vector.Dot.dot

Interface hash: sha256:98e85b682ad6b2c6a8f2d8865f42ae643087bbcc15c7cfc9ea061cede03ad156

Std.Logic.Eq.Eq

Interface hash: sha256:ca4f8520fd678a809c3ebf0bc7fa38d3063ca4d231e79d567de888685449a015