Thm* x: . y: . y y x & x<(y+1) (y+1) | [sfa_doc_nat_sqrt] |
Thm* x,y: . x<y & ( z: . z<x y<z) | [sfa_doc_simple_existential_2] |
Thm* x: . x x = 4 | [sfa_doc_simple_existential_1] |
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* 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* 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* B:(A Prop). ( x:A. B(x))  ( C:Prop. ( x:A. B(x)  C)  C) | [sfa_doc_some_via_so] |
Thm* s:Sexpr(A). ( x:A. s = Inj(x)) ( s1,s2:Sexpr(A). s = Cons(s1;s2)) | [sfa_doc_sexpr_case_thm] |
Thm* f:{f:(   )| x: . f(x) }, i: . i<mu(f)  f(i) | [kleene_minimize_is_lb] |
Thm* f:{f:(   )| x: . f(x) }. f(mu(f)) | [kleene_minimize_is_fp] |
Thm* mu {f:(   )| x: . f(x) }   | [kleene_minimize_wf] |
Thm* f:{f:(   )| x: . f(x) }. f(0)  ( x.f(1+x)) {f:(   )| x: . f(x) } | [kleene_tail] |
Def mod k == x,y: //( m: . x-y = m k) | [sfa_doc_sample_intmod] |