law_of_cosines

Mathlib.Geometry.RightTriangle

Packages

Module

Theorems

750

Declarations

1016

Untrusted sidecar

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Statement

forall (A : Vec), forall (B : Vec), forall (C : Vec), @Eq.{1} RingElem (distSq B C) (sub (add (distSq A B) (distSq A C)) (mul two (dot (vec_sub B A) (vec_sub C A))))

Proof term

fun A => fun B => fun C => @Eq.refl.{1} RingElem (distSq B C)

Constants

Mathlib.Algebra.Ring.RingElem

Interface hash: sha256:29d995d6a38e44a010f577d64428b3272226781f7982e2306784cb3bdc4977ea

Mathlib.Algebra.Ring.add

Interface hash: sha256:70894d2717280dc0e45d28bdc4220a44c51506cccc224ab1f339c97d87eedd41

Mathlib.Algebra.Ring.mul

Interface hash: sha256:80cffe9e7407fc4418c1d4503cb479242aacacfa12e5aeca2efc2f48342545b9

Mathlib.Algebra.Ring.sub

Interface hash: sha256:610fd9b8433ec50fafc78815af652d67661140efa647c079515bd92537e1fbb7

Mathlib.Algebra.Square.two

Interface hash: sha256:f931fa56f65ecd2ecb07571c86b95c2cbdbddcddf2e4174328af33af415996d6

Mathlib.Vector.Basic.Vec

Interface hash: sha256:bc9e713ccaaae78bf5ef428fe3455d47b8f8432e58b79a82bf806866b713e287

Mathlib.Vector.Basic.vec_sub

Interface hash: sha256:2448bcd101acb31d3756f9617d2e06a12117058937c4514c506217480afbccad

Mathlib.Vector.Dot.distSq

Interface hash: sha256:5ac54f1e61b75c804955d1e59695207380bedc448b775db4267dfa4c1feaf8ad

Mathlib.Vector.Dot.dot

Interface hash: sha256:98e85b682ad6b2c6a8f2d8865f42ae643087bbcc15c7cfc9ea061cede03ad156

Std.Logic.Eq.Eq

Interface hash: sha256:ca4f8520fd678a809c3ebf0bc7fa38d3063ca4d231e79d567de888685449a015