The theory of constructive types (principles of logic and mathematics). By Leon Chwistek.

57
12-43 1- {x [(y). f {y, } p.], [. (y) f {y, x} p.]
[12-42-3121]
12 5 1 Jz{z [(x, y)f/{, y, z}l, z[(z) f /x, Y, z]}
Constr. -. 12 1.0-441. D - ({ [f{x, y',}], z [f(x', x, }}}
[025.4] D 1- { [x) / tX, y',;)], [(Y) f {x' Y, 1}
[0o252] D C [(x)f {, y', }],[.(x)f/{Xy', }I ()f{x',' YZ} ]} (1). 121. 0252-412. D - z [f {x, y, z}, z [.f{x, y', z} 1 {' y, z}.]}
[0-252] D 1- C (x [(x, y)f /{ y, z }, [(x, y). f {, y', z} If {x', y, }.]} (2)
-. (i). (2). D -Prop.
12-1 I {y I(xl - ) f,{, x2 y}], y,[(U, X) t {U7 x, y}]}
Constr. 1- 121.0242-261-26-4 D
1- c {y (x, S)a {Uf, x- Y}], y [(X, ). / {U, x ' y'} I fa {v, X, }.}
112-421.0 26 261.J
1- {Y [(z u)fa {U, j}]1, [(x).(C) f( {-5,, '}I fax,, y{,.])
[0-27] 3) 1- { [(!,, u) fa {(, x, y}], y [. (u)f, {, x', y'} I (x) fa {v, x y}. ]}
[12-421.0-26 261.]
1- {Y [(x, U) ta { U, x, Y}], Y [(U) a {U, x', t} | (x).a {VI, X } ]}
1[027] D 1- C{y [( u) fa {, }]y y [(C, ).f { C, x '} fa {v, X.]}
t[0252] D 1- Prop.
We shall use the following abbreviations:
1 -011 c{x y, z}=. _ {x, z}. e{y, z}.
12-012 C{x, y, z, '} =: {x, z'}. {y, z'}: C{z, z'.
dl
Note that, if we take fa{v} for [l{u}] {v}, this is by no
means effected by the simple application of 0'16:but we first take
by 12-0102
u[.f{}.(7): 7 {u} )D {u}.D. {a}3D {a}:.] for u [ f {u}]
and then we apply the direction 0'16 to this function..Automatical construction of assertions.
It is to be remarked that the number of definitions needed
in practice is very great. In this paper we shall not give all definitions explicitly in cases from which any ambiguity is excluded.
We shall also use some simplifications in our construction of ex