(**************************************************************************)
(*  Levy's cube lemma :                                                   *)
(*  (U,V,UV,VU:redexes)  (residuals U V UV) -> (residuals V U VU) ->      *)
(*  (W,WU,WV,WUV:redexes)(residuals W U WU) -> (residuals WU VU WUV) ->   *)
(*                       (residuals W V WV) -> (residuals WV UV WUV).     *)
(**************************************************************************)

Lemma cube :
forall U V UV VU : redexes,
residuals U V UV ->
residuals V U VU ->
forall W WU WV WUV : redexes,
residuals W U WU ->
residuals WU VU WUV -> residuals W V WV -> residuals WV UV WUV.