(** Given two angles a and b, a/2 - b/2 = (a-b)/2 *)

Lemma acute_ghalfa2_sams_suma2__ghalfa123 : forall A B C D E F X Y Z A' B' C' D' E' F' X' Y' Z',
SAMS A' B' C' D' E' F' -> Acute A B C ->
SumA A B C D E F X Y Z -> SumA A' B' C' D' E' F' X' Y' Z' ->
gHalfA D E F D' E' F' -> gHalfA X Y Z X' Y' Z' ->
gHalfA A B C A' B' C'.