let i, j, m, n be Nat; :: thesis: for X being BCK-algebra of i,j,m,n holds X is BCK-algebra of n,j,m,n

let X be BCK-algebra of i,j,m,n; :: thesis: X is BCK-algebra of n,j,m,n

for x, y being Element of X holds Polynom (n,j,x,y) = Polynom (m,n,y,x)

let X be BCK-algebra of i,j,m,n; :: thesis: X is BCK-algebra of n,j,m,n

for x, y being Element of X holds Polynom (n,j,x,y) = Polynom (m,n,y,x)

proof

hence
X is BCK-algebra of n,j,m,n
by Def3; :: thesis: verum
let x, y be Element of X; :: thesis: Polynom (n,j,x,y) = Polynom (m,n,y,x)

Polynom (i,j,x,y) = Polynom (m,n,y,x) by Def3;

hence Polynom (n,j,x,y) = Polynom (m,n,y,x) by Th19; :: thesis: verum

end;Polynom (i,j,x,y) = Polynom (m,n,y,x) by Def3;

hence Polynom (n,j,x,y) = Polynom (m,n,y,x) by Th19; :: thesis: verum