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In L i simboli sono: connettivi primitivi , negazione, implicazione parentesi (,) lettere enunciative A1, A2,...An. Una sequenza finita di simboli si chiama Espressione. FZg-Z,-Z ZZ'$$ $($ ,,,&<Le formule ben formate sono particolari espressioni individuate dalla definizione seguente: (a) Le lettere enunciative sono f.b.f. (b) Se A e B sono f.b.f. lo sono anche (A) e (AB). A: negazione di A; AB: A implica B. .ZHZCZZZ(,x(((('((((((($   Si privilegia un insieme di f.b.f. da chiamare Assiomi. La teoria si dice assiomatica se esiste un procedimento che permette di decidere effettivamente se una fbf un assioma. Nel nostro caso gli assiomi (o, pi precisamente, schemi di assiomi) sono:v<(/$($$ $$@aSchemi di Assiomi di L PA1 (A (BA)) Da A segue ( B implica A). A2 ((A(BC)) ((AB)(AC)) ) Se da A segue (B implica C), da (A implica B) segue (A implica C). A3 ((B A) (( B A) B)). Se da (non B) segue (non A), da ((non B) implica A) segue B.` ((((((((( ($$$ ((((((((((((((((((((Z (((((((((((((((((((((( $<$ ) Regole di inferenza Esiste un insieme finito di relazioni tra fbf dette regole di inferenza. In L abbiamo una sola regola di inferenza, il Modus Ponens (M P): - Date le fbf. A e AB, - B risulta conseguenza diretta di A e AB. ^Z,-ZZ6$$$$$*$ $$$$$$$$$$ $($$$$$$$Z+Q9  Dimostrazione6  Sequenza di formule ben formate i cui elementi sono assiomi o conseguenze dirette di fbf precedenti per mezzo di una delle regole di inferenza (M P).~ ,,,,,,*,,,&V> Teorema 6 QUna fbf A con la propriet che esiste una dimostrazione la cui ultima fbf A. NQ $$D$$(@@  Decidibilit 0 La teoria si dice decidibile quando esiste un procedimento meccanico che permette di stabilire se una qualsiasi fbf un teorema oppure no. :( (r(&q   Conseguenza  `Una fbf A si dice conseguenza di un insieme di fbf. se A l ultima fbf di una sequenza che contiene assiomi, conseguenze dirette e fbf. di G. Si ha, in tal caso, una deduzione di A da G. Si usa scrivere: G | A. Quando G l insieme vuoto, si scrive | A. In quest ultimo caso, A un teorema. .2G4G   V  t*> Esempio di teorema in L Lemma 1.7 | AA. 1) ( (A ((AA)A) ) ( (A(AA)) (AA) ) ) (A2) 2) (A ((AA)A)) (A1) 3) ( (A(AA)) (AA) ) 2), 1), MP 4) ( (A(AA)) (A1) 5) (AA) 4), 3), MP Nelle applicazioni degli schemi di assiomi si sostituisce B con (A A)   # !90C  8Principio d induzione finita Data una proposizione Pn, si supponga che siano soddisfatte le seguenti condizioni: 1) P1 vera; 2) Supposta vera Pn, si riesce a dimostrare che vera anche Pn+1. ___________________ Si pu, allora, affermare che Pn vera per ogni n. Z( (C( (( (2( (<( ((Zap HPrincipio d induzione finita:esempio%$ %La somma dei primi n numeri dispari n2. L affermazione vera per n=1. Supposto, per ipotesi induttiva, che l affermazione sia vera per n numeri dispari (cio che 1+3+...+2n-1= n2), bisogna far vedere che essa risulta vera anche per n+1. T'( (( (:(  HPrincipio d induzione finita:esempio%$ % Infatti, l (n+1)esimo numero dispari si scrive 2(n+1)-1 = 2n+1 e, sommandolo a n2, si ottiene n2+2n+1=(n+1)2\2CU6 66 6 6 6 u Teorema di deduzione (  Se G,A | B allora G | AB. (Se B una conseguenza delle ipotesi G e A, allora AB una conseguenza di G). In particolare, nel caso in cui G l insieme vuoto, si ha che: se A |B allora | AB. (Se B una conseguenza di A, allora AB un teorema).Z Z$$($$$$$$$$($$$$$$$$! #"    Dimostrazione  "Sia B1, B2,...Bn=B una deduzione di B da G,A. Il teorema vero per n=1: - Se B1 un assioma o B1 G, poich anche (B1 (AB1)) un assioma , per MP si ottiene G | AB1. - Se B1 A, per il lemma precedente si ha che |AA e, a maggior ragione, G | AA.6$$$$$$$$$$$$$$,$$$$$$ $$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$$$$$$$$$$$$$$$($$$$$$& ^Per ipotesi induttiva, sia il teorema vero per ogni k<i: G | ABk. Bisogna far vedere che: G | ABi. Se Bi un assioma, Bi G, Bi A, si procede come nel caso i=1.  :(,((((((((,,((((((((((((((((,(((((!(&AmbSe Bi ottenuto per MP da due elementi precedenti della sequenza, essi dovranno assumere la forma Bj e (BjBi) e, per ipotesi induttiva, si avr : | ABj e G | A(BjBi). Ma ((A (BjBi) ) ( (ABj) (ABi) )) un assioma e, per MP applicato due volte, si otterr, finalmente, G | ABi.|GtG G(((^(((((((((((%((((((((((((((((((((((((((((((((((((((((((((((((K(6(((((((( c. cProposizione 1.11  Ogni teorema di L una tautologia. Infatti, gli assiomi sono tautologie e l MP fa passare da tautologie a tautologie. T%ZVZZZz( }Corollario 1.9a)  AB, BC | AC Dimostrazione 1) A B ip 2) BC ip. 3) A ip. 4) B 1, 3, MP 5) C 2, 4, MP _________________ AB, BC , A | C Per il teorema di deduzione AB, BC | AC ZZZZ  'Z,Corollario 1.9b) A (BC), B | AC Dimostrazione 1) A (BC) ip 2) A ip. 3) B ip. 4) BC 1, 2, MP 5) C 3, 4, MP _________________ A (BC), B, A | C Per il teorema di deduzione A(BC), B | AC  ZZ Z5 Lemma 1.10   a) | BB. 1) (B B)((BB) B) A3 2) ( B B) lemma 1.7 3) ( B B) B 1, 2, cor. 1.9b 4) B (B B ) A1 5) B B 3, 4, cor.1.9a4!x:6%  Lemma 1.10 Fb) | B B. 1) (BB)((BB) B) A3 2) (B B) Lemma1.10a 3) ( B B) B 1, 2, MP 4) B (B B ) A1 5) B B 3,4,cor. 1.9a # 2%( $C) | A (AB). 1) A ip. 2) A ip. 3) A (BA) A1 4) A(BA) A1 5) BA 2, 3, MP 6) BA 1, 4 MP 7) (BA) ((BA)B) A3 8) (BA) B 6, 7, MP 9) B 5, 8, MP ________________________________________ Perci A, A | B e, per il teorema di deduzione, | A(AB). BZZ0(3FC$<p>$@X"P$ d) | (BA) (AB) 1) BA ip. 2) A ip. 3) (BA ) (BA)B A3 4) A(BA) A1 5) (BA)B 1, 3, MP 6) AB 4, 5, cor. 1.9a 7) B 2, 6, MP Perci (BA), A |B) e, con due successive applicazioni del teorema di deduzione | (BA) (AB) ZZ/7),>JC@X7e)| (AB)(BA) 1)AB ip. 2)A A parte a) 3)AB 1, 2, cor.1.9a) 4)BB parte b) 5)AB 3, 4, cor.1.9a) 6)(AB) (BA) parte d) 7)(BA) 5, 6. MP _____________________________________ Perci AB | BA e, per il teorema di deduzione | (AB) (BA). 4ZZZ" )1.0b:&<f) | A(B (AB) 1) A ip. 2) AB ip. 3) B 1, 2, MP Perci A, AB | B e, per il teorema di deduzione, | A((AB)B). 4)A((AB)B) 5)((AB)B).(B(AB)) Lemma 1.10 e) 6)A(B (AB) 4, 5, cor.1.9a xK )    %@;" g) | (AB)((AB)B) 1) (AB) ip. 2) AB ip. 3) (AB) (BA) parte e) 4) B A 1, 3, MP 5) (AB) (BA) parte e) 6) B A 2, 5, MP 7) (B A)(B A)B A3 8) (B A)B 6, 7, MP 9) B 4, 8, MP Perci AB, AB| A e, per il t. di deduzione | (AB)((AB)B). 2ZZZ 5"&6  ,A,@L2! Lemma 1.12  Sia A una fbf e B1,..., Bk le lettere enunciative che occorrono in A. Per una data assegnazione di valori di verit a B1,..., Bk, siano B 1,..., B k tali che B i sia Bi se Bi assume il valore di verit V, B i sia Bi se Bi assume il valore F. In maniera analoga A sar A se quest ultima assume il valore V, A sar A se A assume il valore F. Allora B 1,..., B k | A . x   )3          "   Z  d&( Esempio di applicazione del lemma 1.12  )( Dimostrazione del lemma 1.12 nSe n=0 allora A una lettera enunciative B1 e il lemma si riduce a B1| B1 e B1 | B1. Supponiamo che il lemma valga per tutte le fbf con un numero di connettivi primitivi j < n: ((( (( (((( (((( ((((((( (]($&/)!$1) A B. B ha meno occorrenze di A . a) B ha il valore V e A ha il valore F. B B e A A. Per ipotesi induttiva B 1,..., B k | B e, poich B B** si ha, per MP, B 1,..., B k | B, cio B 1,..., B k |A ** lemma 1.10b<D(((((((((((((( (( ( (( ((((( ((( (( ((((($$( (, (( (((((($ *"Lb) B ha il valore F e A il valore V. B B e A A. Per ipotesi induttiva B 1,..., B k | B, cio B 1,..., B k | A ,,,,,,+,,,,,,,,,,$, ,, ,,,,,,,, ,, ,,,,,,, +#2) A (B C). Poich B e C hanno meno occorrenze di A per ipotesi induttiva si avr B 1,..., B k | B e B 1,..., B k | C . a) B ha il valore F e A il valore V. B 1,..., B k | B e B 1,..., B k | (BC)***. Ma (BC) A , per cui B 1,..., B k | A *** @ZZ((((((( (* ( (( ((((((( (( (((((( (((((( ((( (( ((((((( ( (( (((((((( (( $$$$$$ $ $$ $$$$$$( A,$6b)C ha il valore V e, quindi, A il valore V. B 1,..., B k x C e, per lo schema d assiomi A1 e MP, B 1,..., B k x BC. Quindi, B 1,..., B k x A . 0(((( (( ((( (( ((((((*( (( (((((((( ( (( ((((((( -%rc) C ha il valore F e B il valore V, quindi A ha il valore F. B 1,..., B k | C, quindi, B 1,..., B k | (BC)****. Poich (BC) A , si ha la tesi. **** .,,,,, ,,,,,,, ,, ,,,,,,,, ,, ,,,,,,,,,,, ,,,,,,,,,,( /'Teorema di completezza  NSe una formula ben formata una tautologia, allora essa un teorema di L. OM0 O.&  Dimostrazione : essendo A una tautologia, essa ha sempre il valore V. Il lemma 1.12 d le due relazioni di deduzione: B 1,...,B k-1, Bk | A B 1,...,B k-1,Bk|A. Per il teorema di deduzione si ha B 1,...,B k-1 | Bk A B 1,...,B k-1 | BkA. Si ha, quindi, B 1,...,B k-1 | A.***** Applicando k volte questo procedimento si ottiene | A. ***** bI7.4t?n<1Corollario 1.15 Il sistema L consistente, cio non esiste alcuna fbf. A tale che tanto A quanto A siano teoremi di L. Dimostrazione. Ogni teorema di L una tautologia e, dato che la negazione di una tautologia non pu essere, a sua volta, una tautologia, si ottiene la tesi.  ((( (((((((((&4=2Si osservi che L consistente se e solo se non tutte le sue fbf sono teoremi. Infatti, se L consistente , le negazioni dei teoremi sono fbf che non sono teoremi. . *,@=L>3Viceversa, se L inconsistente (cio, se ammette come teoremi una fbf e la sua negazione), allora, 1) A ip. 2) A ip. 3) A (AB) lemma 1.10c 4) A B 1, 3, MP 5) B 2, 4, MP Zk((((( ((((((((((((((((ZC<g?4Perci, se L inconsistente, qualsiasi formula ben formata B un teorema di L. Una teoria nella quale non tutte le fbf sono teoremi detta assolutamente consistente.. V<((Q(((&u3A5Indipendenza di assiomi Proposizione 1.16. Ogni schema di assiomi A1-A3 indipendente. Dimostrazione. Indipendenza di A1. Si considerino le seguenti tavole: @@$$6$ B6 Negazione $   X A A 0 1 1 1 2 0 F,,,%, -C7 Condizionale  D8(Se una formula ben formata A assume sempre il valore 0, diciamo che A una scelta. L MP fa passare da fbf scelte a fbf scelte. Gli schemi di assiomi A2 e A3 sono scelti, mentre A1 non scelto. 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N F ___PPT10& .+FD'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*3%(D' =-s6Bwipe(left)*<3<*3+8+0+0 + 0 ((  (r ( S a 0  a  2 ( Na ?"`  K1( H ( 0޽h ? y___PPT10Y+D='  = @B + 0N0 K(    C 0a <$ 0 a  (EMU2  NIa ?"0  K2( xB  BD?" ` H  0޽h ? ___PPT10.+FDF'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*_%(D' =-s6Bwipe(left)*<3<*_D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*_%(D' =-s6Bwipe(left)*<3<*_D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*+8+0+0 + 0N0 (    C G( <$ 0 a  2  NM( ?"0  K3( H  0޽h ? ___PPT10.+FD'  = @B DA' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* +8+0+0 + 0N0 K(  l  C xSa `  a    C xTa 0 <$ 0 a  R  <lYa  P@00 KRITORNO H  0޽h ? ___PPT10.+FDF'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*<%(D' =-s6Bwipe(left)*<3<*<D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*<`%(D' =-s6Bwipe(left)*<3<*<`D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-s6Bwipe(left)*<3<*`D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*)%(D' =-s6Bwipe(left)*<3<*)+8+0+0 + 0N0  #(   l  C (ya pP  a    C (za  <$ 0 a  2  N{a ?"0 @ K4( H  0޽h ? ___PPT10.+FDf'  = @B D!' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* '%(D' =-s6Bwipe(left)*<3<* 'D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<* 'K%(D' =-s6Bwipe(left)*<3<* 'KD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* K%(D' =-s6Bwipe(left)*<3<* KD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' =-s6Bwipe(left)*<3<* +8+0+ 0 + 0N0 $^( r $l $ C a P  a   $ C a <$ 0 a  &x=/[cH $ 0޽h ? nf___PPT10F.+FD'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*$%(D' =-s6Bwipe(left)*<3<*$+8+0+$0 + 0N0 (D(  (l ( C ( P  (   ( C D( <$ 0 (  H ( 0޽h ? nf___PPT10F.+FD'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*(Q%(D' =-s6Bwipe(left)*<3<*(Q+8+0+(0 +  0N0 ,D(  ,l , C a P  a   , C a 0<$ 0 a  H , 0޽h ? ___PPT10.+FDf'  = @B D!' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*,$%(D' =-s6Bwipe(left)*<3<*,$D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*,$E%(D' =-s6Bwipe(left)*<3<*,$ED' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*,Eg%(D' =-s6Bwipe(left)*<3<*,EgD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*,g%(D' =-s6Bwipe(left)*<3<*,gD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-s6Bwipe(left)*<3<*,+8+0+,0 +  0N0 p0D(  0l 0 C вa 0  a   0 C (a <$ 0 a  H 0 0޽h ? ___PPT10.+FD&'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*0.%(D' =-s6Bwipe(left)*<3<*0.D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*0.`%(D' =-s6Bwipe(left)*<3<*0.`D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*0`%(D' =-s6Bwipe(left)*<3<*0`D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-s6Bwipe(left)*<3<*0D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-s6Bwipe(left)*<3<*0D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*0%(D' =-s6Bwipe(left)*<3<*0D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*00%(D' =-s6Bwipe(left)*<3<*00+8+0+00 +$  0N0 ` 4g( w 4l 4 C  a P  a   4 C d <$ 0 a   Y  " 4 <Xd  @00 USchemi di assiomi xB 4 BD?" xB 4 BD?"``H 4 0޽h ?   ___PPT10f .+FD '  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*41%(D' =-s6Bwipe(left)*<3<*41D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*41Z%(D' =-s6Bwipe(left)*<3<*41ZD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*4Z%(D' =-s6Bwipe(left)*<3<*4ZD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*4U%(D' =-s6Bwipe(left)*<3<*4UD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*4U%(D' =-s6Bwipe(left)*<3<*4UD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%((/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*4%(D' =-s6Bwipe(left)*<3<*4+8+0+40 +  0N0 P8D(  8l 8 C 5)   a   8 C +) p<$ 0 )  H 8 0޽h ? ___PPT10.+FD&'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*8U%(D' =-s6Bwipe(left)*<3<*8UD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*8Uf%(D' =-s6Bwipe(left)*<3<*8UfD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*8f%(D' =-s6Bwipe(left)*<3<*8fD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*8%(D' =-s6Bwipe(left)*<3<*8+8+0+80 +r   0N0 @<D( w <l < C )   )   < C ) <$ 0 )  H < 0޽h ? N F ___PPT10& .+FD'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*<J%(D' =-s6Bwipe(left)*<3<*<JD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*<J%(D' =-s6Bwipe(left)*<3<*<J+8+0+<0 +R 0N0 0DD( w Dl D C @ ) P  )   D C () <$ 0 )  H D 0޽h ? . & ___PPT10 .+FD '  = @B Da ' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*D2%(D' =-s6Bwipe(left)*<3<*D2D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*D2D%(D' =-s6Bwipe(left)*<3<*D2DD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*DDu%(D' =-s6Bwipe(left)*<3<*DDu+8+0+D0 + 0N0  HD( ( Hl H C `%d 0  d   H C t'd <$ 0 d  H H 0޽h ? ___PPT10.+FDf'  = @B D!' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*H#%(D' =-s6Bwipe(left)*<3<*H#D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*H#v%(D' =-s6Bwipe(left)*<3<*H#vD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*Hv%(D' =-s6Bwipe(left)*<3<*HvD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*H%(D' =-s6Bwipe(left)*<3<*HD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*H %(D' =-s6Bwipe(left)*<3<*H +8+0+H0 + 0N0 LU(  Ll L C 8?d p  d   L C 7d <$ 0 d   " L <@d p 0@00 USCHEMI DI ASSIOMI H L 0޽h ? ___PPT10.+FDF'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*L/%(D' =-s6Bwipe(left)*<3<*L/D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*L/K%(D' =-s6Bwipe(left)*<3<*L/KD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*LKk%(D' =-s6Bwipe(left)*<3<*LKkD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*Lk%(D' =-s6Bwipe(left)*<3<*LkD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-s6Bwipe(left)*<3<*LD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*L%(D' =-s6Bwipe(left)*<3<*L+8+0+L0 +~ 0N0 @8P(  P P C Ud <$ 0 d  H P 0޽h ? ___PPT10.+FDF'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*P'%(D' =-s6Bwipe(left)*<3<*P'D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*P'E%(D' =-s6Bwipe(left)*<3<*P'ED' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*PE]%(D' =-s6Bwipe(left)*<3<*PE]D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*P]l%(D' =-s6Bwipe(left)*<3<*P]lD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*Pl%(D' =-s6Bwipe(left)*<3<*PlD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*P%(D' =-s6Bwipe(left)*<3<*P+8+0+P0 + 0N0 @8T(  T T C ad <$ 0 d  H T 0޽h ? ___PPT10.+FDf'  = @B D!' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-s6Bwipe(left)*<3<*TD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-s6Bwipe(left)*<3<*TD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*T%(D' =-s6Bwipe(left)*<3<*TD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*T'%(D' =-s6Bwipe(left)*<3<*T'D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*T'2%(D' =-s6Bwipe(left)*<3<*T'2+8+0+T0 +r  0N0 XD( ( Xl X C d P  d   X C td p <$ 0 d  H X 0޽h ? N F ___PPT10& .+FD'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*X%%(D' =-s6Bwipe(left)*<3<*X%D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*X%{%(D' =-s6Bwipe(left)*<3<*X%{+8+0+X0 +/ 0N0 ;3\( w \l \ C ,td p  d   \ C ud <$ 0 d  R \ <wd @@00 KRITORNO xB \ BD?"` ` H \ 0޽h ? .,&,___PPT10,.+FD+'  = @B Da+' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-s6Bwipe(left)*<3<*\D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-s6Bwipe(left)*<3<*\D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\/%(D' =-s6Bwipe(left)*<3<*\/D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\/@%(D' =-s6Bwipe(left)*<3<*\/@D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\@U%(D' =-s6Bwipe(left)*<3<*\@UD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\Uo%(D' =-s6Bwipe(left)*<3<*\UoD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\o%(D' =-s6Bwipe(left)*<3<*\oD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%((/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-s6Bwipe(left)*<3<*\D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(-/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-s6Bwipe(left)*<3<*\D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(2/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-s6Bwipe(left)*<3<*\D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(7/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*\%(D' =-s6Bwipe(left)*<3<*\+8+0+\0 +Y/ 0N0 `K( w `l ` C Ȟd p  d   ` C ld <$ 0 d  R ` <d  Qq@00 KRITORNO H ` 0޽h ? .,&,___PPT10,.+FD+'  = @B Da+' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-s6Bwipe(left)*<3<*`D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`"%(D' =-s6Bwipe(left)*<3<*`"D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`"8%(D' =-s6Bwipe(left)*<3<*`"8D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`8W%(D' =-s6Bwipe(left)*<3<*`8WD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`Wv%(D' =-s6Bwipe(left)*<3<*`WvD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`v%(D' =-s6Bwipe(left)*<3<*`vD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-s6Bwipe(left)*<3<*`D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%((/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-s6Bwipe(left)*<3<*`D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(-/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-s6Bwipe(left)*<3<*`D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(2/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*`%(D' =-s6Bwipe(left)*<3<*`D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(7/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*` %(D' =-s6Bwipe(left)*<3<*` +8+0+`0 + 0N0 IAd(  dl d C *   d   d C d P<$ 0 *   d 6d  P@00 TCorollario 1.9a)  d 6Hd  P@00 TCorollario 1.9b)  d 6d P@00 KAssiomi xB d BD?"0 H d 0޽h ? 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N(F(___PPT10&(.+FD''  = @B D'' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-s6Bwipe(left)*<3<*xD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*x?%(D' =-s6Bwipe(left)*<3<*x?D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*x?c%(D' =-s6Bwipe(left)*<3<*x?cD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*xc%(D' =-s6Bwipe(left)*<3<*xcD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-s6Bwipe(left)*<3<*xD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-s6Bwipe(left)*<3<*xD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-s6Bwipe(left)*<3<*xD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%((/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-s6Bwipe(left)*<3<*xD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(-/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*x%(D' =-s6Bwipe(left)*<3<*xD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(2/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*xK%(D' =-s6Bwipe(left)*<3<*xK+8+0+x0 +E3 0N0 P|W(   | | C Lr <$ 0   R | <t P @00 KRITORNO xB | BD?" 0 H | 0޽h ? 00___PPT10/.+FD/'  = @B DA/' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-s6Bwipe(left)*<3<*|D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|P%(D' =-s6Bwipe(left)*<3<*|PD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|P%(D' =-s6Bwipe(left)*<3<*|PD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-s6Bwipe(left)*<3<*|D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-s6Bwipe(left)*<3<*|D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|!%(D' =-s6Bwipe(left)*<3<*|!D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|!W%(D' =-s6Bwipe(left)*<3<*|!WD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%((/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|Wz%(D' =-s6Bwipe(left)*<3<*|WzD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(-/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|z%(D' =-s6Bwipe(left)*<3<*|zD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(2/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|%(D' =-s6Bwipe(left)*<3<*|D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(7/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|2%(D' =-s6Bwipe(left)*<3<*|2D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(</%,( < +D' =1:Bvisible*o3>+B#style.visibility<*|2H%(D' =-s6Bwipe(left)*<3<*|2H+8+0+|0 +2 0N0 @D(  l  C       C  `<$ 0   H  0޽h ? ___PPT10.+FD'  = @B DA' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*G%(D' =-s6Bwipe(left)*<3<*GD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*G%(D' =-s6Bwipe(left)*<3<*GD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*]%(D' =-s6Bwipe(left)*<3<*]D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*]x%(D' =-s6Bwipe(left)*<3<*]x+8+0+0 +w  0N0  t( w l  C ȥ     0 0A 2??6 H 2$D 0  XB  0D` `XB  0D`` XB  0D XB  0DP P  XB @ 0D XB  0D XB  0D XB  0D  XB  0D  XB  0DPXB  0DPP B  s *޽h ? )!___PPT10.+3!>D'  = @B D' = @BA?%,( < +O%,( < +D' =%(Ds' =%(D' =4@BBBB%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*+r  0N0 PD(    l  C  P     C  <$ 0   H  0޽h ? N F ___PPT10& .+FD'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*[%(D' =-s6Bwipe(left)*<3<*[D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*[%(D' =-s6Bwipe(left)*<3<*[+8+0+0 +\!  0N0 nf`(    C  `<$ 0   0j,~"  <| 0 @@00 N LEMMA 1.10   H  0޽h ? ~v___PPT10V.+FD'  = @B D' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*(%(D' =-s6Bwipe(left)*<3<*(D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*(V%(D' =-s6Bwipe(left)*<3<*(VD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*V%(D' =-s6Bwipe(left)*<3<*VD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*Dh ' =%(D ' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%("/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*+8+0+0 + !0N0 `X@( w   C , <$ 0 -  ,Q }H  0޽h ? ___PPT10.+FDf'  = @B D!' = @BA?%,( < +O%,( < +D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*>%(D' =-s6Bwipe(left)*<3<*>D' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*>U%(D' =-s6Bwipe(left)*<3<*>UD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*Up%(D' =-s6Bwipe(left)*<3<*UpD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*p%(D' =-s6Bwipe(left)*<3<*pD' =%(D' =%(D(' =A@BBBB0B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' =-s6Bwipe(left)*<3<*+8+0+0 +R6 "0N0 qi0( '00H(   c $lG ?<$ 0 -  *!MU]e  6TI  @^00 Q Lemma 1.10c)  H  0޽h ? q3i3___PPT10I3.+`nD2' L = @B D2' = @BA?%,( < +O%,( < +D' =%(D+' =%(D' =A@BBBB0B@B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' K=+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' K=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D+' =%(D' =A@BBBB0B@B%(E' =4 B`BPB`B?<*%( /%,( < +D' =1:Bvisible*o3>+B#style.visibility<*B%(D' K=+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*BD' K=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*BD' =%(D+' =%(D' =A@BBBB0B@B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*Bk%(D' K=+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*BkD' K=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*BkD' =%(D+' =%(D' =A@BBBB0B@B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*k%(D' K=+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*kD' K=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*kD' =%(D+' =%(D' =A@BBBB0B@B%(E' =4 B`BPB`B?<*%(/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' K=+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' K=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D+' =%(D' =A@BBBB0B@B%(E' =4 B`BPB`B?<*%(#/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*%(D' K=+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' K=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*D' =%(D+' =%(D' =A@BBBB0B@B%(E' =4 B`BPB`B?<*%()/%,( < +D' =1:Bvisible*o3>+B#style.visibility<* %(D' K=+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' K=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* D' =%(D+' =%(D' =A@BBBB0B@B%(E' =4 B`BPB`B?<*%(//%,( < +D' =1:Bvisible*o3>+B#style.visibility<* :%(D' K=+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* :D' K=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<* :D' =%(D+' =%(D' =A@BBBB0B@B%(E' =4 B`BPB`B?<*%(5/%,( < +D' =1:Bvisible*o3>+B#style.visibility<*:@%(D' K=+4 8?dCB1+#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*:@D' K=+4 8?dCB0-#ppt_h/2BCB#ppt_yB*Y3>B ppt_y<*:@+8+0+0 +d #0   ( FF l  C 4O-  -  H  0޽h ?  $0 :2( w   C S 0 -  ,5>aiqy  6U  @t00 P Lemma 1.10f)   H  0޽h ?  %0 ( w l  C \ P   l  C ]    H  0޽h ? j &0 ( w l  C -  -    6h- 0@@ @z00 P Lemma 1.10g)   H  0޽h ?  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