Thm* A:Type, a:A, xs:A List. (a list xs) Prop | [sfa_doc_inlist_wf] |
Thm* x: List, y: . y greater-bounds x Prop | [sfa_doc_greater_list_bound_wf] |
Thm* P:(A Prop). ( x:A. Dec(P(x)))  ( f:(A  ). x:A. P(x)  f(x)) | [sfa_doc_bool_vs_decidable_fun] |
Thm* Dec(P)  ( b: . P  b) | [sfa_doc_bool_vs_decidable] |
Thm* x: , f:(   ). f zero beyond x Prop | [sfa_doc_props_as_types_example1_wf] |
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* R:(A (A List) Prop Prop).
Thm* P:((A List) Prop).
Thm* (P(nil)  Q) & ( a:A, x:A List. P(a.x)  R(a,x,P(x))) | [sfa_doc_listind_via_so] |
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* False  ( C:Prop. C) | [sfa_doc_false_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:Type(given A). B(given A) Type | [sfa_doc_guarded_typing] |
Thm* A:Prop, B:Prop(given A). (A  B) Prop | [sfa_doc_imp_typing] |
Thm* A:Type, P:(A Prop), n: , X:(A^n). ( u in X: A^n. P(u)) Prop | [sfa_doc_ntuple_contains_wf] |
Thm* A:Prop, B:Prop(given A). (A & B) Prop | [sfa_doc_and_typing] |
Thm* P:(A Prop), B:(x:A Type(given P(x))).
Thm* x:{u:A| P(u) } B(x) =ext x:A B(x)(given P(x)) | [sfa_doc_exteq_gfun2] |
Thm* B:(A Prop), C:({u:A| B(u) } Type).
Thm* x:{u:A| B(u) } C(x) =ext x:A C(x)(given B(x)) | [sfa_doc_exteq_gfun] |
Thm* P:(A Prop). {x:A| P(x) } Prop =ext x:A Prop(given P(x)) | [sfa_doc_exteq_gprop] |
Def HigherConsequence{i}(P) == {X:Prop{i'}| P  X } | [sfa_doc_le_parm_sample_def] |