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403.1999969 0 0 336.9600067 0 239.0399933 cm
/Im0 Do
Q
q
403.1999969 0 0 239.0399933 0 0 cm
/Im1 Do
Q
BT
/T1_0 1 Tf
0.05 Tc 3 Tr 10.7428 0 0 9.5 20.47 538.75 Tm
(Proposition )Tj
9.7138 0 0 9.5 80.12 538.75 Tm
(10. )Tj
/T1_1 1 Tf
0.013 Tc 9.6 0 0 9.6 99.43 538.75 Tm
(Player )Tj
0 Tc 3.158 0 Td
(A )Tj
-0.0022 Tc 1.218 0 Td
(wins )Tj
0.0305 Tc 2.325 0 Td
(when )Tj
0 Tc 2.644 0 Td
(p )Tj
/T1_2 1 Tf
8.7 0 0 8.7 198.4 538.75 Tm
(= )Tj
/T1_0 1 Tf
-0.0133 Tc 9.5 0 0 9.5 210 538.75 Tm
(25; )Tj
/T1_1 1 Tf
0.0093 Tc 9.6 0 0 9.6 226.69 538.75 Tm
(Player )Tj
/T1_0 1 Tf
0 Tc 9.5 0 0 9.5 256.46 538.75 Tm
(B )Tj
/T1_1 1 Tf
0.004 Tc 9.6 0 0 9.6 267.62 538.75 Tm
(wins )Tj
-0.035 Tc 9.3996 0 0 9.6 290.12 538.75 Tm
(for )Tj
9.5983 0 0 9.6 304.86 538.75 Tm
(all )Tj
0.05 Tc 9.8301 0 0 9.6 318.52 538.75 Tm
(other )Tj
0 Tc 9.6 0 0 9.6 344.84 538.75 Tm
(p )Tj
/T1_2 1 Tf
-0.035 Tc 6.0689 0 0 11.6 354.32 538.75 Tm
(== )Tj
/T1_0 1 Tf
0 Tc 9.5 0 0 9.5 20.48 527.23 Tm
(4 )Tj
0.05 Tc 9.5165 0 0 9.5 28.24 527.23 Tm
(mod )Tj
-0.035 Tc 9.1253 0 0 9.5 49.76 527.23 Tm
(7. )Tj
0.05 Tc 10.4037 0 0 9.5 20.47 510.49 Tm
(Proof: )Tj
0.0308 Tc 9.5 0 0 9.5 55.58 510.49 Tm
(Player )Tj
0 Tc 3.128 0 Td
(A )Tj
-0.0026 Tc 1.157 0 Td
(wins )Tj
0.0377 Tc 2.331 0 Td
(when )Tj
/T1_3 1 Tf
0 Tc 8.1 0 0 8.1 143.85 510.49 Tm
(p )Tj
/T1_0 1 Tf
11.3 0 0 11.3 152.94 510.49 Tm
(= )Tj
-0.0187 Tc 9.5 0 0 9.5 164.28 510.49 Tm
(25, )Tj
0.0328 Tc 1.732 0 Td
(by )Tj
0.0294 Tc 1.497 0 Td
(playing )Tj
-0.035 Tc 10.0035 0 0 10.9 229.62 510.49 Tm
([M)Tj
/T1_2 1 Tf
0 Tc 6.1 0 0 6.1 241.21 509.23 Tm
(I)Tj
0.682 0.207 Td
(, )Tj
/T1_1 1 Tf
0.0341 Tc 10.6 0 0 10.6 249.41 510.49 Tm
(M3,., )Tj
/T1_0 1 Tf
0.05 Tc 11.7028 0 0 10.6 275.8 510.49 Tm
(-,.] )Tj
-0.0099 Tc 9.5 0 0 9.5 295.82 510.49 Tm
(from )Tj
0.026 Tc 2.443 0 Td
(\(23,1,0,0\); )Tj
0.0111 Tc -31.423 -1.194 Td
(which )Tj
0.0012 Tc 2.823 0 Td
(works )Tj
-0.0051 Tc 2.806 0 Td
(by )Tj
0.0427 Tc 1.34 0 Td
(Proposition )Tj
0.0135 Tc 5.394 0 Td
(7\(iv\). )Tj
/T1_2 1 Tf
0.05 Tc 12.7834 0 0 9.2 163.99 499.15 Tm
(If )Tj
/T1_1 1 Tf
0 Tc 9.1 0 0 9.1 173.65 499.15 Tm
(p )Tj
/T1_2 1 Tf
-0.035 Tc 6.0689 0 0 11.6 181.52 499.15 Tm
(== )Tj
/T1_0 1 Tf
0 Tc 9.5 0 0 9.5 191.84 499.15 Tm
(4 )Tj
0.05 Tc 9.6126 0 0 9.5 199.96 499.15 Tm
(mod )Tj
0 Tc 9.5 0 0 9.5 221.66 499.15 Tm
(7 )Tj
0.0419 Tc 0.796 0 Td
(and )Tj
/T1_1 1 Tf
0 Tc 9.1 0 0 9.1 246.91 499.15 Tm
(p )Tj
/T1_3 1 Tf
-0.035 Tc 4.0033 0 0 7.6 254.6 499.15 Tm
(=1= )Tj
/T1_0 1 Tf
8.7518 0 0 9.5 264.73 499.15 Tm
(25 )Tj
0.05 Tc 9.6378 0 0 9.5 276.82 499.15 Tm
(then )Tj
0.0308 Tc 9.5 0 0 9.5 298.4 499.15 Tm
(Player )Tj
/T1_2 1 Tf
0 Tc 8.8 0 0 8.8 327.77 499.15 Tm
(B )Tj
/T1_0 1 Tf
0.05 Tc 10.1855 0 0 9.5 337.54 499.15 Tm
(starts )Tj
0.0328 Tc 9.5 0 0 9.5 20.35 487.81 Tm
(by )Tj
0.0199 Tc 1.478 0 Td
(playing )Tj
0.045 Tc 3.575 0 Td
([M)Tj
/T1_2 1 Tf
0 Tc 6.3001 0 0 6.3001 80.11 486.01 Tm
(I)Tj
0.603 0.286 Td
(, )Tj
0.05 Tc 12.4635 0 0 6.3001 88.09 487.81 Tm
(-,.,., )Tj
10.2547 0 0 6.3001 114.75 487.81 Tm
(.]. )Tj
12.7834 0 0 9.2 130.51 487.81 Tm
(If )Tj
/T1_1 1 Tf
0 Tc 9.1 0 0 9.1 141.07 487.81 Tm
(p )Tj
/T1_2 1 Tf
8.7 0 0 8.7 149.62 487.81 Tm
(= )Tj
/T1_0 1 Tf
9.5 0 0 9.5 160.52 487.81 Tm
(4 )Tj
0.04 Tc 0.923 0 Td
(or )Tj
/T1_1 1 Tf
0 Tc 9.1 0 0 9.1 181.57 487.81 Tm
(p )Tj
/T1_2 1 Tf
8.7 0 0 8.7 190.66 487.81 Tm
(= )Tj
/T1_0 1 Tf
-0.035 Tc 9.0645 0 0 9.5 202.19 487.81 Tm
(11 )Tj
0.05 Tc 9.6378 0 0 9.5 215.44 487.81 Tm
(then )Tj
0 Tc 9.5 0 0 9.5 237.74 487.81 Tm
(B )Tj
-0.0067 Tc 1.064 0 Td
(now )Tj
-0.0026 Tc 2.141 0 Td
(wins )Tj
0.0138 Tc 2.333 0 Td
(by )Tj
0.05 Tc 9.5767 0 0 9.5 303.98 487.81 Tm
(Proposition )Tj
0 Tc 9.5 0 0 9.5 357.15 487.81 Tm
(1 )Tj
0.05 Tc 9.6349 0 0 9.5 20.6 476.11 Tm
(and )Tj
0.0333 Tc 9.5 0 0 9.5 38.84 476.11 Tm
(Proposition )Tj
0 Tc 5.259 0 Td
(6 )Tj
0.0113 Tc 0.788 0 Td
(respectively. )Tj
0.039 Tc 5.751 0 Td
(Otherwise )Tj
0.05 Tc 9.6991 0 0 9.5 196.18 476.11 Tm
(the )Tj
0.0228 Tc 9.5 0 0 9.5 212.5 476.11 Tm
(game )Tj
0.05 Tc 9.612 0 0 9.5 236.74 476.11 Tm
(state )Tj
-0.0246 Tc 9.5 0 0 9.5 259.3 476.11 Tm
(is )Tj
/T1_1 1 Tf
-0.035 Tc 9.1112 0 0 10.1 268.92 476.11 Tm
(\(p )Tj
/T1_0 1 Tf
0 Tc 10.1 0 0 10.1 278.52 476.11 Tm
(-)Tj
0.05 Tc 9.9541 0 0 9.5 286.88 476.11 Tm
(4,2,0,0\) )Tj
9.8699 0 0 9.5 325.16 476.11 Tm
(and )Tj
9.5756 0 0 9.5 343.81 476.11 Tm
(play )Tj
0.0191 Tc 9.5 0 0 9.5 20.53 464.41 Tm
(proceeds )Tj
0.0127 Tc 4.062 0 Td
(as )Tj
-0.0282 Tc 1.232 0 Td
(follows. )Tj
-0.005 Tc -5.022 -1.175 Td
(\(a\) )Tj
0 Tc 9.3 0 0 9.3 39.74 453.25 Tm
(B )Tj
0.015 Tc 9.5 0 0 9.5 49.15 453.25 Tm
(plays )Tj
0.0328 Tc 9.3 0 0 9.3 73.76 453.25 Tm
([M)Tj
/T1_2 1 Tf
0 Tc 6.3001 0 0 6.3001 85.15 451.45 Tm
(I)Tj
0.689 0.286 Td
(, )Tj
/T1_3 1 Tf
9.3 0 0 9.3 93.3 453.25 Tm
(M)Tj
6.3001 0 0 6.3001 102.85 451.63 Tm
(2)Tj
0.05 Tc 12.449 0 0 6.3001 107.38 453.25 Tm
(,.,., )Tj
/T1_0 1 Tf
-0.035 Tc 8.4853 0 0 10.9 129.33 453.25 Tm
(e] )Tj
0.0111 Tc 9.5 0 0 9.5 139.49 453.25 Tm
(which )Tj
0.0253 Tc 2.861 0 Td
(reaches )Tj
/T1_1 1 Tf
-0.035 Tc 9.5556 0 0 10.3 200.87 453.25 Tm
(\(p )Tj
/T1_0 1 Tf
0.05 Tc 9.9285 0 0 9.5 220.56 453.25 Tm
(6,0,2,0\) )Tj
0.0211 Tc 9.5 0 0 9.5 258.57 453.25 Tm
(or )Tj
0.0037 Tc 1.202 0 Td
(wins )Tj
0.0328 Tc 2.257 0 Td
(by )Tj
0.05 Tc 9.5767 0 0 9.5 304.7 453.25 Tm
(Proposition )Tj
0 Tc 9.5 0 0 9.5 357.17 453.25 Tm
(5 )Tj
/T1_1 1 Tf
-0.035 Tc 8.889 0 0 10.1 40.14 441.55 Tm
(\(p )Tj
/T1_0 1 Tf
0 Tc 11.3 0 0 11.3 50.7 441.55 Tm
(= )Tj
0.0014 Tc 9.5 0 0 9.5 60.69 441.55 Tm
(18\), )Tj
0.039 Tc 1.963 0 Td
(Proposition )Tj
0.0025 Tc 5.356 0 Td
(7\(ii\) )Tj
/T1_1 1 Tf
-0.035 Tc 9.1112 0 0 10.1 151.2 441.55 Tm
(\(p )Tj
/T1_0 1 Tf
0 Tc 11.3 0 0 11.3 162.12 441.55 Tm
(= )Tj
0.0215 Tc 9.5 0 0 9.5 172.15 441.55 Tm
(32\), )Tj
0.04 Tc 2.029 0 Td
(or )Tj
0.0408 Tc 1.256 0 Td
(Proposition )Tj
0 Tc 5.348 0 Td
(8 )Tj
/T1_1 1 Tf
-0.035 Tc 9.1112 0 0 10.1 262.62 441.55 Tm
(\(p )Tj
/T1_0 1 Tf
5.9683 0 0 10.8 273.57 441.55 Tm
(2:: )Tj
-0.0038 Tc 9.5 0 0 9.5 283.21 441.55 Tm
(39\). )Tj
-0.0051 Tc -27.436 -1.194 Td
(\(b\) )Tj
0.029 Tc 1.807 0 Td
(From )Tj
/T1_1 1 Tf
0.05 Tc 11.4178 0 0 10.1 65.65 430.21 Tm
(\(p-6,0,2,0\) )Tj
/T1_0 1 Tf
0 Tc 9.3 0 0 9.3 125.6 430.21 Tm
(B )Tj
0.015 Tc 9.5 0 0 9.5 136.45 430.21 Tm
(plays )Tj
/T1_1 1 Tf
-0.035 Tc 9.9801 0 0 10.6 162.17 430.21 Tm
([M)Tj
/T1_3 1 Tf
0 Tc 6.3001 0 0 6.3001 173.95 428.77 Tm
(2)Tj
/T1_1 1 Tf
0.05 Tc 12.9156 0 0 10.6 178.6 430.21 Tm
(,-,M)Tj
/T1_3 1 Tf
0 Tc 6.3001 0 0 6.3001 201.14 428.77 Tm
(3)Tj
/T1_1 1 Tf
0.05 Tc 11.8803 0 0 10.6 205.96 430.21 Tm
(,e,M)Tj
/T1_3 1 Tf
0 Tc 6.3001 0 0 6.3001 228.11 428.77 Tm
(5)Tj
0.64 0.229 Td
(] )Tj
/T1_0 1 Tf
0.0419 Tc 9.5 0 0 9.5 238.76 430.21 Tm
(and )Tj
0.0095 Tc 1.999 0 Td
(reaches )Tj
/T1_1 1 Tf
-0.035 Tc 9.3334 0 0 10.1 291.95 430.21 Tm
(\(p )Tj
/T1_0 1 Tf
0.05 Tc 10.4038 0 0 9.5 312.35 430.21 Tm
(6,0,0,0\) )Tj
9.5989 0 0 9.5 353.25 430.21 Tm
(or )Tj
/T1_1 1 Tf
-0.034 Tc 9.1 0 0 9.1 40.14 418.87 Tm
(\(p )Tj
/T1_0 1 Tf
0 Tc 1.115 0 Td
(-)Tj
0.05 Tc 9.9027 0 0 9.5 59.11 418.87 Tm
(9,0,3,0\). )Tj
0.0465 Tc 9.5 0 0 9.5 100.9 418.87 Tm
(The )Tj
0.0208 Tc 2.025 0 Td
(former )Tj
-0.0246 Tc 3.204 0 Td
(is )Tj
0.0326 Tc 0.983 0 Td
(equivalent )Tj
0.05 Tc 9.8224 0 0 9.5 206.08 418.87 Tm
(to )Tj
0 Tc 9.5 0 0 9.5 217.88 418.87 Tm
(a )Tj
0.0165 Tc 0.798 0 Td
(game )Tj
0.05 Tc 9.5943 0 0 9.5 249.7 418.87 Tm
(starting )Tj
0.0474 Tc 9.5 0 0 9.5 284.93 418.87 Tm
(with )Tj
/T1_1 1 Tf
0 Tc 9.1 0 0 9.1 306.13 418.87 Tm
(p )Tj
/T1_2 1 Tf
-0.035 Tc 5.7409 0 0 11.6 313.65 418.87 Tm
(== )Tj
/T1_0 1 Tf
0 Tc 9.3 0 0 9.3 323.87 418.87 Tm
(5 )Tj
0.05 Tc 9.7087 0 0 9.5 332.44 418.87 Tm
(mod )Tj
-0.035 Tc 9.386 0 0 9.5 354.5 418.87 Tm
(7, )Tj
0.0111 Tc 9.5 0 0 9.5 39.59 407.53 Tm
(which )Tj
0.027 Tc 2.858 0 Td
(Player )Tj
/T1_2 1 Tf
0 Tc 8.8 0 0 8.8 95.75 407.53 Tm
(B )Tj
/T1_0 1 Tf
-0.0026 Tc 9.5 0 0 9.5 105.65 407.53 Tm
(wins )Tj
0.0138 Tc 2.276 0 Td
(by )Tj
0.0446 Tc 1.397 0 Td
(Proposition )Tj
-0.035 Tc 9.1292 0 0 9.5 192.14 407.53 Tm
(9. )Tj
-0.024 Tc 9.5 0 0 9.5 23.65 396.19 Tm
(\(c\) )Tj
0.029 Tc 1.694 0 Td
(From )Tj
/T1_1 1 Tf
-0.035 Tc 9.1112 0 0 10.1 66.78 396.19 Tm
(\(p )Tj
/T1_0 1 Tf
0 Tc 10.1 0 0 10.1 78.36 396.19 Tm
(-)Tj
0.05 Tc 10.035 0 0 9.5 88.45 396.19 Tm
(9,0,3,0\) )Tj
/T1_2 1 Tf
0 Tc 8.8 0 0 8.8 128.69 396.19 Tm
(B )Tj
/T1_0 1 Tf
0.0103 Tc 9.5 0 0 9.5 140.77 396.19 Tm
(plays )Tj
/T1_1 1 Tf
-0.035 Tc 9.9801 0 0 10.6 167.39 396.19 Tm
([M)Tj
0 Tc 6.5001 0 0 6.5001 179.07 394.75 Tm
(2)Tj
0.05 Tc 12.0704 0 0 10.6 183.82 396.19 Tm
(,e,M)Tj
0 Tc 6.5001 0 0 6.5001 206.22 394.75 Tm
(4)Tj
0.05 Tc 13.1225 0 0 10.6 211.19 396.19 Tm
(,.,M)Tj
0 Tc 6.5001 0 0 6.5001 233.22 394.75 Tm
(5)Tj
0.622 0.222 Td
(] )Tj
/T1_0 1 Tf
0.05 Tc 9.6041 0 0 9.5 244.42 396.19 Tm
(to )Tj
0.0185 Tc 9.5 0 0 9.5 257.75 396.19 Tm
(reach )Tj
/T1_1 1 Tf
-0.035 Tc 9.1112 0 0 10.1 285.12 396.19 Tm
(\(p )Tj
/T1_0 1 Tf
0 Tc 10.1 0 0 10.1 296.7 396.19 Tm
(-)Tj
0.05 Tc 10.0778 0 0 9.5 307.27 396.19 Tm
(12,0,4,0\) )Tj
9.5989 0 0 9.5 353.25 396.19 Tm
(or )Tj
/T1_1 1 Tf
-0.035 Tc 9.1112 0 0 10.1 40.14 384.67 Tm
(\(p )Tj
/T1_0 1 Tf
0 Tc 10.1 0 0 10.1 50.64 384.67 Tm
(-)Tj
0.05 Tc 9.9027 0 0 9.5 59.47 384.67 Tm
(9,0,1,0\). )Tj
0.037 Tc 9.5 0 0 9.5 101.44 384.67 Tm
(The )Tj
0.05 Tc 9.8479 0 0 9.5 120.52 384.67 Tm
(latter )Tj
-0.035 Tc 9.3682 0 0 9.5 146.62 384.67 Tm
(is )Tj
0.0326 Tc 9.5 0 0 9.5 155.96 384.67 Tm
(equivalent )Tj
0.05 Tc 9.8224 0 0 9.5 202.12 384.67 Tm
(to )Tj
9.5625 0 0 9.5 213.82 384.67 Tm
(the )Tj
0.0285 Tc 9.5 0 0 9.5 230.23 384.67 Tm
(position )Tj
-0.0094 Tc 3.748 0 Td
(two )Tj
-0.0069 Tc 1.876 0 Td
(moves )Tj
0.05 Tc 9.5981 0 0 9.5 311.5 384.67 Tm
(into )Tj
0 Tc 9.5 0 0 9.5 331.64 384.67 Tm
(a )Tj
0.05 Tc 9.6333 0 0 9.5 339.58 384.67 Tm
(game )Tj
0.0064 Tc 9.5 0 0 9.5 39.59 373.15 Tm
(which )Tj
0.05 Tc 9.5616 0 0 9.5 66.82 373.15 Tm
(started )Tj
0.0347 Tc 9.5 0 0 9.5 98.99 373.15 Tm
(with )Tj
/T1_1 1 Tf
0 Tc 9.1 0 0 9.1 120.37 373.15 Tm
(p )Tj
/T1_2 1 Tf
-0.035 Tc 5.9049 0 0 11.6 128.79 373.15 Tm
(== )Tj
/T1_0 1 Tf
0 Tc 9.5 0 0 9.5 139.37 373.15 Tm
(5 )Tj
0.05 Tc 9.6126 0 0 9.5 147.04 373.15 Tm
(mod )Tj
-0.035 Tc 9.1253 0 0 9.5 168.74 373.15 Tm
(7. )Tj
0.0274 Tc 9.5 0 0 9.5 181.24 373.15 Tm
(Again, )Tj
0.0138 Tc 3.3 0 Td
(by )Tj
0.0352 Tc 1.416 0 Td
(Proposition )Tj
0 Tc 5.336 0 Td
(9 )Tj
-0.035 Tc 9.1156 0 0 9.5 284.93 373.15 Tm
(we )Tj
-0.0077 Tc 9.5 0 0 9.5 299.14 373.15 Tm
(know )Tj
0.05 Tc 9.6245 0 0 9.5 324.14 373.15 Tm
(Player )Tj
/T1_2 1 Tf
0 Tc 9 0 0 9 354.95 373.15 Tm
(B )Tj
/T1_0 1 Tf
-0.0123 Tc 9.5 0 0 9.5 39.77 361.45 Tm
(wins. )Tj
0.0043 Tc -1.792 -1.194 Td
(\(d\) )Tj
0.0353 Tc 1.788 0 Td
(From )Tj
/T1_1 1 Tf
-0.035 Tc 8.889 0 0 9.4 64.62 350.11 Tm
(\(p )Tj
/T1_0 1 Tf
0.05 Tc 10.7785 0 0 9.5 74.21 350.11 Tm
(-12,0,4,0\) )Tj
-0.0242 Tc 9.5 0 0 9.5 125 350.11 Tm
(for )Tj
/T1_1 1 Tf
0 Tc 9.4 0 0 9.4 139.1 350.11 Tm
(p )Tj
/T1_0 1 Tf
11.3 0 0 11.3 146.82 350.11 Tm
(= )Tj
0.0252 Tc 9.5 0 0 9.5 156.89 350.11 Tm
(IS, )Tj
0 Tc 1.576 0 Td
(B )Tj
0.0292 Tc 1.009 0 Td
(plays )Tj
/T1_3 1 Tf
0.05 Tc 9.9652 0 0 9.3 206.63 350.11 Tm
([M)Tj
0 Tc 6.2 0 0 6.2 218.22 348.67 Tm
(5)Tj
0.739 0.232 Td
(, )Tj
/T1_2 1 Tf
0.05 Tc 11.441 0 0 6.2 226.49 350.11 Tm
(., )Tj
/T1_3 1 Tf
0 Tc 9.3 0 0 9.3 235.5 350.11 Tm
(M)Tj
6.2 0 0 6.2 244.52 348.67 Tm
(3)Tj
0.735 0.232 Td
(, )Tj
/T1_0 1 Tf
0.05 Tc 8.4619 0 0 7.8001 252.99 350.11 Tm
(e, )Tj
0.0137 Tc 9.5 0 0 9.5 261.86 350.11 Tm
(MIl )Tj
0.05 Tc 9.5174 0 0 9.5 280.34 350.11 Tm
(and )Tj
-0.0152 Tc 9.5 0 0 9.5 298.25 350.11 Tm
(wins )Tj
0.05 Tc 10.0347 0 0 9.5 319.15 350.11 Tm
(by )Tj
9.619 0 0 9.5 332.96 350.11 Tm
(Propo\255)Tj
0.0272 Tc 9.5 0 0 9.5 39.65 338.59 Tm
(sition )Tj
-0.035 Tc 8.9895 0 0 9.5 65.4 338.59 Tm
(5. )Tj
0.0057 Tc 9.5 0 0 9.5 76.82 338.59 Tm
(For )Tj
/T1_1 1 Tf
0 Tc 9.1 0 0 9.1 93.37 338.59 Tm
(p )Tj
/T1_0 1 Tf
-0.035 Tc 6.1549 0 0 10.8 101.49 338.59 Tm
(2:: )Tj
-0.0192 Tc 9.5 0 0 9.5 110.95 338.59 Tm
(32, )Tj
/T1_2 1 Tf
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