Thm* exists( f:hind  hind. and(one_one(f),not(onto(f)))) | [hinfinity_ax] |
Thm* 'b,'a:S.
Thm* all
Thm* ( P:'a  hbool. all
Thm* ( P:'a  hbool. ( rep:'b  'a. equal
Thm* ( P:'a  hbool. ( rep:'b  'a. (type_definition(P,rep)
Thm* ( P:'a  hbool. ( rep:'b  'a. ,and
Thm* ( P:'a  hbool. ( rep:'b  'a. ,(all
Thm* ( P:'a  hbool. ( rep:'b  'a. ,(( x':'b. all
Thm* ( P:'a  hbool. ( rep:'b  'a. ,(( x':'b. ( x'':'b. implies
Thm* ( P:'a  hbool. ( rep:'b  'a. ,(( x':'b. ( x'':'b. (equal
Thm* ( P:'a  hbool. ( rep:'b  'a. ,(( x':'b. ( x'':'b. ((rep(x')
Thm* ( P:'a  hbool. ( rep:'b  'a. ,(( x':'b. ( x'':'b. (,rep(x''))
Thm* ( P:'a  hbool. ( rep:'b  'a. ,(( x':'b. ( x'':'b. ,equal(x',x''))))
Thm* ( P:'a  hbool. ( rep:'b  'a. ,,all
Thm* ( P:'a  hbool. ( rep:'b  'a. ,,( x:'a. equal
Thm* ( P:'a  hbool. ( rep:'b  'a. ,,( x:'a. (P(x)
Thm* ( P:'a  hbool. ( rep:'b  'a. ,,( x:'a. ,exists
Thm* ( P:'a  hbool. ( rep:'b  'a. ,,( x:'a. ,( x':'b. equal
Thm* ( P:'a  hbool. ( rep:'b  'a. ,,( x:'a. ,( x':'b. (x
Thm* ( P:'a  hbool. ( rep:'b  'a. ,,( x:'a. ,( x':'b. ,rep(x'))))))))) | [htype_definition_wd] |
Thm* 'a:S.
Thm* equal
Thm* (cond
Thm* , t:hbool. t1:'a. t2:'a. select
Thm* , t:hbool. t1:'a. t2:'a. ( x:'a. and
Thm* , t:hbool. t1:'a. t2:'a. ( x:'a. (implies(equal(t,t),equal(x,t1))
Thm* , t:hbool. t1:'a. t2:'a. ( x:'a. ,implies(equal(t,f),equal(x,t2))))) | [hcond_def] |
Thm* 'a:S.
Thm* equal
Thm* (exists_unique
Thm* , P:'a  hbool. and
Thm* , P:'a  hbool. (exists(P)
Thm* , P:'a  hbool. ,all
Thm* , P:'a  hbool. ,( x:'a. all( y:'a. implies(and(P(x),P(y)),equal(x,y)))))) | [hexists_unique_def] |
Thm* equal
Thm* (and
Thm* , t1:hbool. t2:hbool. all( t:hbool. implies(implies(t1,implies(t2,t)),t))) | [hand_def] |