Typos.

diff --git a/matita/matita/lib/tutorial/chapter12.ma b/matita/matita/lib/tutorial/chapter12.ma
index 47f8a971f76e7460457d2bc56d84fa8b807cc17e..a4f47c1ffa7c38cca91315c5747385c9fb5a8628 100644 (file)
--- a/matita/matita/lib/tutorial/chapter12.ma
+++ b/matita/matita/lib/tutorial/chapter12.ma
@@ -72,7 +72,7 @@ definition Z: setoid ≝
  @(injective_plus_r … H4)
 qed.
 
-(* The two integers (0,1) and (1,2) are equal up to â\89\9d, written
+(* The two integers (0,1) and (1,2) are equal up to â\89\83, written
    〈0,1〉 ≃ 〈1,2〉. Unfolding the notation, that corresponds to
    eqrel ? (eq_setoid ?) 〈0,1〉 〈1,2〉 which means that the two
    pairs are to be compare according to the equivalence relation
@@ -140,7 +140,7 @@ record morphism (I,O: setoid) : Type[0] ≝ {
  ; mor_proper: proper … mor_carr
  }.
 
-(* We introduce a notation for morhism using a long arrow. *)
+(* We introduce a notation for morphism using the symbols of an arrow followed by a dot. *)
 notation "hvbox(I break ⤞ O)"
   right associative with precedence 20
 for @{ 'morphism $I $O }.
@@ -150,7 +150,7 @@ interpretation "morphism" 'morphism I O = (morphism I O).
 (* By declaring mor_carr as a coercion it is possible to write f x for
    mor_carr f x in order to apply a morphism f to an argument. *)
 
-(* Example: oppositive of an integer number. We first implement the function
+(* Example: opposite of an integer number. We first implement the function
   over Z and then lift it to a morphism. The proof obligation is to prove
   properness. *)
 definition opp: Z → Z ≝ λc.〈\snd c,\fst c〉.
@@ -178,7 +178,7 @@ unification hint 0 ≔ x:Z ;
 
 (* Example: we state that opp is proper and we will prove it without using
  automation and without referring to OPP. When we apply the universal mor_proper
- property of morhisms, Matita looks for the morphism associate to opp x and
+ property of morphisms, Matita looks for the morphism associate to opp x and
  finds it thanks to the second unification hint above, completing the proof. *)
 example ex2: ∀x,y. x ≃ y → opp x ≃ opp y.
  #x #y #EQ @mor_proper @EQ

diff --git a/matita/matita/lib/tutorial/chapter13.ma b/matita/matita/lib/tutorial/chapter13.ma
index 3ff16855e67af8e6aeff2641480cebeb2ee79cad..1971b956ee9421eaac258dadf5c5512253e7032b 100644 (file)
--- 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 ≝