let p be natural prime number ; for a being integer number holds
( Leg (a,p) = 1 or Leg (a,p) = 0 or Leg (a,p) = - 1 )
let a be integer number ; ( Leg (a,p) = 1 or Leg (a,p) = 0 or Leg (a,p) = - 1 )
assume A1:
( Leg (a,p) <> 1 & Leg (a,p) <> 0 )
; Leg (a,p) = - 1
a gcd p = 1
hence
Leg (a,p) = - 1
by A1, Def4; verum