Example of Extension Axiom
t(x1, x2, x3)
=
x1 ¹ x2 Æ x2 ¹ x3 Æ x1 ¹ x3 Æ
R(x1,x2)
Æ R(x2,x3) Æ R(x2,x2)
Æ
: R(x1, x1)
Æ : R(x2, x1)
Æ …
x1
x2
x3
s(x1, x2, x3,
z) =
t(x1,
x2,
x3)
Æ
z ¹ x1 Æ z ¹ x2 Æ z ¹ x3 Æ
R(z,x1) Æ R(x3,z) Æ R(z,z) Æ
: R(x1,
z) Æ : (z, x2) Æ …
z