distance_zero_iff_eq

Mathlib.Geometry.Metric

Packages

Module

Theorems

750

Declarations

1016

Untrusted sidecar

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Statement

forall (A : Vec), forall (B : Vec), forall (P : Prop), forall (mk : forall (forward : forall (h : @Eq.{1} RingElem (dist A B) zero), @Eq.{1} Vec A B), forall (backward : forall (h : @Eq.{1} Vec A B), @Eq.{1} RingElem (dist A B) zero), P), P

Proof term

fun A => fun B => fun P => fun mk => mk (fun (h : @Eq.{1} RingElem (dist A B) zero) => @Vec.rec.{0} (fun (x : Vec) => @Eq.{1} Vec x B) (@Vec.rec.{0} (fun (y : Vec) => @Eq.{1} Vec Vec.unit y) (@Eq.refl.{1} Vec Vec.unit) B) A) (fun (h : @Eq.{1} Vec A B) => @Eq.refl.{1} RingElem (dist A B))

Constants

Mathlib.Algebra.Ring.RingElem

Interface hash: sha256:29d995d6a38e44a010f577d64428b3272226781f7982e2306784cb3bdc4977ea

Mathlib.Algebra.Ring.zero

Interface hash: sha256:acd114675ba5b92c602836fd317cdd80e63659c99ff34e05341dda09002571d5

Mathlib.Geometry.Metric.dist

Interface hash: sha256:c347b9c90c3a22c05c9d1015de25a718c6eb51773118496c16c6552049b5f462

Mathlib.Vector.Basic.Vec

Interface hash: sha256:bc9e713ccaaae78bf5ef428fe3455d47b8f8432e58b79a82bf806866b713e287

Std.Logic.Eq.Eq

Interface hash: sha256:ca4f8520fd678a809c3ebf0bc7fa38d3063ca4d231e79d567de888685449a015