Thm* Y( f,x. if x= 0 1 else x f(x-1) fi)     | [sfa_doc_ycomb_factorial_typing] |
Thm* ( f,x. if x= 0 1 else x f(x-1) fi) ( k: . ( k  )  (k+1)  ) | [sfa_doc_factbody_polytyping] |
Thm* f,g:(   ).
Thm* ( x: . f zero beyond x) & ( x: . g zero beyond x)
Thm* 
Thm* ( x: . ( i.if i even f(i) else g(i) fi) zero beyond x) | [sfa_doc_alternate_zero_beyond] |
Thm* f:(   ).
Thm* ( n: . f(n) = 0)
Thm* 
Thm* ( n: . if f(n)= 0 False else C:Prop{1}. C fi) Prop{1} | [sfa_doc_predicativity_sample8] |
Def i steps of e from a == if i= 0 a else e(i-1 steps of e from a) fi
Def (recursive) | [sfa_doc_sequence_rel] |
Def max(a;b) == if a< b b else a fi | [sfa_doc_max_int] |
Def A^n == if n= 0 Unit ; n= 1 A else A (A^(n-1)) fi (recursive) | [sfa_doc_ntuple] |
Def x! == if x= 0 1 else x (x-2)! fi (recursive) | [sfa_doc_factorial2] |
Def x! == if x= 0 1 else x (x-1)! fi (recursive) | [sfa_doc_factorial] |
Def mu(f) == if f(0) 0 else 1+mu( x.f(1+x)) fi (recursive) | [kleene_minimize] |