From 836e4f30514bceb27394604bbfbae31a62723dae Mon Sep 17 00:00:00 2001 From: Claudio Sacerdoti Coen Date: Tue, 21 Oct 2014 12:20:39 +0000 Subject: [PATCH] Typos. --- matita/matita/lib/tutorial/chapter12.ma | 8 ++++---- matita/matita/lib/tutorial/chapter13.ma | 5 ++--- 2 files changed, 6 insertions(+), 7 deletions(-) diff --git a/matita/matita/lib/tutorial/chapter12.ma b/matita/matita/lib/tutorial/chapter12.ma index 47f8a971f..a4f47c1ff 100644 --- 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 ≝, written +(* The two integers (0,1) and (1,2) are equal up to ≃, 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 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 ≝ -- 2.39.2