Thm* f:( D:Type. D (D List)), A:Type, a,x:A. x list f(a)  x = a | [sfa_doc_type_poly_mem_const] |
Thm* a:A, w:{a:A} List. z:A. z list w  z = a | [sfa_doc_inlist_singleton_const] |
Thm* P:(A Prop). ( x:A. Dec(P(x)))  ( f:(A  ). x:A. P(x)  f(x)) | [sfa_doc_bool_vs_decidable_fun] |
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* P Q  ( x: . (x = 0  P) & (x 0  Q)) | [sfa_doc_or_dec] |
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] |
Thm* a,b:A. a = b  ( P:(A Prop). P(a)  P(b)) | [sfa_doc_equal_via_so] |
Thm* B:(A Prop). ( x:A. B(x))  ( C:Prop. ( x:A. B(x)  C)  C) | [sfa_doc_some_via_so] |
Thm* (A  B)  ( C:Prop. ((A  B)  (B  A)  C)  C) | [sfa_doc_iff_via_so] |
Thm* A  ( C:Prop. A  C) | [sfa_doc_not_via_so] |
Thm* A B  ( C:Prop. (A  C)  (B  C)  C) | [sfa_doc_or_via_so] |
Thm* A & B  ( C:Prop. (A  B  C)  C) | [sfa_doc_and_via_so] |
Thm* A:Prop, B:Prop(given A). (A  B) Prop | [sfa_doc_imp_typing] |
Thm* A:Type, s:Sexpr(A). Size(s) = 1   sexprAtom(s) A | [sfa_doc_sexpr_atom_wf] |
Thm* s:Sexpr(A). Size(s) 1   Size(sexprCdr(s))<Size(s) | [sfa_doc_sexprcdrsize] |
Thm* s:Sexpr(A). Size(s) 1   Size(sexprCar(s))<Size(s) | [sfa_doc_sexprcarsize] |
Thm* n: . n 2  (A^n) = A (A^(n-1)) | [sfa_doc_ntuple_is_prod] |
Thm* k: . 0<k & (2 k)<1  2<k | [sfa_doc_cand_example] |
Thm* f:{f:(   )| x: . f(x) }, i: . i<mu(f)  f(i) | [kleene_minimize_is_lb] |
Thm* f:{f:(   )| x: . f(x) }. f(0)  ( x.f(1+x)) {f:(   )| x: . f(x) } | [kleene_tail] |
Def f zero beyond x == y: . x<y  f(y) = 0  | [sfa_doc_props_as_types_example1] |
Def HigherConsequence{i}(P) == {X:Prop{i'}| P  X } | [sfa_doc_le_parm_sample_def] |
Def Induction for x: . P(x) == P(0) & ( x: . P(x)  P(x+1))  ( x: . P(x)) | [sfa_doc_indscheme] |