X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Flib%2Ftutorial%2Fchapter13.ma;h=1971b956ee9421eaac258dadf5c5512253e7032b;hb=836e4f30514bceb27394604bbfbae31a62723dae;hp=3ff16855e67af8e6aeff2641480cebeb2ee79cad;hpb=636db4e12452d2ebce318b36cf5c41d30e4d9c29;p=helm.git diff --git a/matita/matita/lib/tutorial/chapter13.ma b/matita/matita/lib/tutorial/chapter13.ma index 3ff16855e..1971b956e 100644 --- a/matita/matita/lib/tutorial/chapter13.ma +++ b/matita/matita/lib/tutorial/chapter13.ma @@ -104,8 +104,7 @@ coercion R_to_fun : ∀r:R. ℕ → Q ≝ r on _r:R to ?. (* Adding two real numbers just requires pointwise addition of the approximations. The proof that the resulting sequence is Cauchy is the standard one: to obtain an approximation up to eps it is necessary to approximate both - summands up to eps/2. The proof that the function is well defined w.r.t. the - omitted equivalence relation is also omitted. *) + summands up to eps/2. *) definition Rplus_: R_ → R_ → R_ ≝ λr1,r2. mk_R_ (λn. r1 n + r2 n) …. #eps @@ -156,7 +155,7 @@ record div_trace: Type[0] ≝ ; div_well_formed: ∀n. next (div_tr n) (div_tr (S n)) }. -(* The previous definition of trace is not very computable: we cannot write +(* The previous definition of trace is not computable: we cannot write a program that given an initial state returns its trace. To write that function, we first write a computable version of next, called step. *) definition step: state → option state ≝