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[7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] Overfull \hbox (3.55002pt too wide) in paragraph at lines 15544--15544 []$\OT1/cmr/m/n/10 [[][\OT1/cmss/m/n/10 x\OT1/cmr/m/n/10 ] [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^ ^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML /cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [[][\OT1/cmss/m/n/10 x\OT1/cmr/m/n/ 10 ] [] [[] []| [] [75] Overfull \hbox (9.77327pt too wide) in paragraph at lines 15991--15991 []$\OT1/cmr/m/n/10 [ragged right expansion [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/ n/10 t\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n /10 c\OML/cmm/m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; 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\OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 H []| [] Overfull \hbox (19.41252pt too wide) in paragraph at lines 22465--23921 []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][][][][], $[\OMS/cms y/m/n/10 I [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/c mss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr /m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/1 0 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OM S/cmsy/m/n/10 I [] []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][] [][][], $[\OMS/cmsy/m/n/10 J [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm /m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 J []| [] Overfull \hbox (19.11818pt too wide) in paragraph at lines 22465--23921 []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][][][][], $[\OMS/cms y/m/n/10 K [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/c mss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr /m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/1 0 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OM S/cmsy/m/n/10 K [] []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][] [][][], $[\OMS/cmsy/m/n/10 L [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm /m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 L []| [] Overfull \hbox (35.94852pt too wide) in paragraph at lines 22465--23921 []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][][][][], $[\OMS/cms y/m/n/10 M [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/c mss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr /m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/1 0 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OM S/cmsy/m/n/10 M [] []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][] [][][], $[\OMS/cmsy/m/n/10 N [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm /m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 N []| [] Overfull \hbox (24.44037pt too wide) in paragraph at lines 22465--23921 []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][][][][], $[\OMS/cms y/m/n/10 O [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/c mss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr /m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/1 0 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OM S/cmsy/m/n/10 O [] []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][] [][][], $[\OMS/cmsy/m/n/10 P [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm /m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 P []| [] Overfull \hbox (25.85706pt too wide) in paragraph at lines 22465--23921 []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][][][][], $[\OMS/cms y/m/n/10 Q [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/c mss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr /m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/1 0 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OM S/cmsy/m/n/10 Q [] []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][] [][][], $[\OMS/cmsy/m/n/10 R [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm /m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 R []| [] Overfull \hbox (19.21637pt too wide) in paragraph at lines 22465--23921 []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][][][][], $[\OMS/cms y/m/n/10 S [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/c mss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr /m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/1 0 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OM S/cmsy/m/n/10 S [] []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][] [][][], $[\OMS/cmsy/m/n/10 T [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm /m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 T []| [] Overfull \hbox (19.42085pt too wide) in paragraph at lines 22465--23921 []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][][][][], $[\OMS/cms y/m/n/10 U [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/c mss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr /m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/1 0 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OM S/cmsy/m/n/10 U [] []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][] [][][], $[\OMS/cmsy/m/n/10 V [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm /m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 V []| [] Overfull \hbox (32.55704pt too wide) in paragraph at lines 22465--23921 []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][][][][], $[\OMS/cms y/m/n/10 W [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/c mss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr /m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/1 0 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OM S/cmsy/m/n/10 W [] []\OT1/cmr/m/n/10 ]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][] [][][], $[\OMS/cmsy/m/n/10 X [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm /m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [\OMS/cmsy/m/n/10 X []| [] [91] [92] [93] [94] [95] [96] [97] Overfull \hbox (19.95831pt too wide) in paragraph at lines 27545--27630 \OT1/cmr/m/n/10 As an ex-am-ple of use, $[proof(\OMS/cmsy/m/n/10 d8[]\OT1/cmr/m /n/10 : \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :\OMS/cmsy/m/n/1 0 U[]\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 E\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 d[]e\ OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 T\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OT1/c mr/m/n/10 )) [] [] \OMS/cmsy/m/n/10 ` 8[]\OT1/cmr/m/n/10 : \OML/cmm/m/it/10 ^^U \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :\OMS/cmsy/m/n/10 U[]\OT1/cmr/m/n/10 (\OMS/c msy/m/n/10 E\OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 d[]e\OML/cmm/m/it/10 ; \OT1/cmss/ m/n/10 T\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OT1/cmr/m/n/10 )) []| [] [98] Overfull \hbox (29.77301pt too wide) in paragraph at lines 28716--28716 []$\OT1/cmr/m/n/10 [Remainder [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm /m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/ m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/ 10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\ OT1/cmr/m/n/10 [Remainder [] HeadPair[] [] Transitivity[] []| [] [99] [100] [101] [102] [103] [104] [105] Overfull \hbox (1.64801pt too wide) in paragraph at lines 33510--33510 []$\OT1/cmr/m/n/10 [\OT1/cmss/m/n/10 p \OT1/cmr/m/n/10 proves \OT1/cmss/m/n/10 t [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/1 0 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr/m/n/10 ( \OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/10 ; \OT1/ cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OT1/cmss/m/ n/10 p \OT1/cmr/m/n/10 proves \OT1/cmss/m/n/10 t [] \OT1/cmr/m/n/10 proof(\OMS/ cmsy/m/n/10 d\OT1/cmss/m/n/10 p\OMS/cmsy/m/n/10 e\OML/cmm/m/it/10 ; \OMS/cmsy/m /n/10 d\OT1/cmss/m/n/10 t\OMS/cmsy/m/n/10 e\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 )]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )]$[][][][][] | [] [106] [107] Overfull \hbox (9.83144pt too wide) in paragraph at lines 34543--34543 []$\OT1/cmr/m/n/10 [[[]\OT1/cmss/m/n/10 x\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 y\O T1/cmr/m/n/10 ] [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\ OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT 1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m /it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [[[]\OT1/cmss/m/n/10 x\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 y\OT1/cmr/m/n/10 ] [] [\OT1/cmss/m/n/10 x [] y\OT1/cmr/m/n/10 ]]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n/10 )] $[][][][][] | [] Overfull \hbox (48.99413pt too wide) in paragraph at lines 34874--34874 []$\OT1/cmr/m/n/10 [[\OT1/cmss/m/n/10 x[]y\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 z\ OT1/cmr/m/n/10 ] [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U \OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\O T1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/ m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/1 0 [[\OT1/cmss/m/n/10 x[]y\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 z\OT1/cmr/m/n/10 ] [] [\OT1/cmss/m/n/10 x[]y\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 z \OMS/cmsy/m/n/10 `| [] [108] Overfull \hbox (168.41162pt too wide) in paragraph at lines 35162--35162 \OT1/cmr/m/n/10 error[](\OMS/cmsy/m/n/10 d[]\OT1/cmr/m/n/10 Circular []proof\O ML/cmm/m/it/10 : []\OT1/cmr/m/n/10 Circle []includes[][]\OMS/cmsy/m/n/10 e\OM L/cmm/m/it/10 ; \OT1/cmss/m/n/10 p[]i[][][][][]\OT1/cmr/m/n/10 ))\OML/cmm/m/it/ 10 ; \OMS/cmsy/m/n/10 V[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 r\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 p\OML/cmm/m/it/10 ; \OT1/ cmss/m/n/10 p\OT1/cmr/m/n/10 )))\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 V[]\OT1/cmr /m/n/10 (\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 r\OML/cmm/m/it/1 0 ; \OT1/cmss/m/n/10 p\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 T\OT1/cmr/m/n/10 ))\O ML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 V[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 c\OML/cm m/m/it/10 ; \OT1/cmss/m/n/10 x\OT1/cmr/m/n/10 ))\OML/cmm/m/it/10 ; \OT1/cmss/m/ n/10 c[]r[][][][][][][]r[]\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c[]\OT1/cmr/m/n/10 0[])]$[][][][][] | [] [109] Overfull \hbox (10.96158pt too wide) in paragraph at lines 35915--35915 \OT1/cmr/m/n/10 error[](\OMS/cmsy/m/n/10 d[]\OT1/cmr/m/n/10 Reference []to [] unproved []lemma[]\OMS/cmsy/m/n/10 e\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 p\OT1/ cmr/m/n/10 )\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 T\OT1/cmr/m/n/10 )))\OML/cmm/m/ it/10 ; \OT1/cmss/m/n/10 p[][]\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; \OT1/cmss/m/n /10 p[][]\OT1/cmr/m/n/10 )\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 p[][]\OT1/cmr/m/n /10 ))\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 V[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 p[][]\OT1/cmr/m/n/10 )))]$[][][][][] | [] [110] [111] Overfull \hbox (50.07213pt too wide) in paragraph at lines 36874--36874 \OT1/cmss/m/n/10 s[][] \OMS/cmsy/m/n/10 ` \OT1/cmr/m/n/10 Cut(\OT1/cmss/m/n/10 s[][][][][][][][]\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 r\OT1/cmr/m/n/10 ))\OML/cm m/m/it/10 ; \OT1/cmr/m/n/10 rule[](\OT1/cmss/m/n/10 s[][]\OML/cmm/m/it/10 ; \OT 1/cmss/m/n/10 t\OT1/cmr/m/n/10 )))\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 ([]stmt[ ]\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s[][]\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c \OT1/cmr/m/n/10 )[][])))\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 ([]stmt[]\OML/cmm/ m/it/10 ; \OT1/cmss/m/n/10 p[][]\OT1/cmr/m/n/10 )[][])]$[][][][][] | [] [112] Overfull \hbox (110.91122pt too wide) in paragraph at lines 37365--37365 []$\OT1/cmr/m/n/10 [[\OT1/cmss/m/n/10 x[]y\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 z\ OT1/cmr/m/n/10 ] [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U \OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\O T1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/ m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/1 0 [[\OT1/cmss/m/n/10 x[]y\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 z\OT1/cmr/m/n/10 ] [] [\OT1/cmss/m/n/10 x[]y\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 z\OT1/cmr/m/n/10 ][ []\OT1/cmss/m/n/10 y\OT1/cmr/m/n/10 : Rule tactic]]\OMS/cmsy/m/n/10 e\OT1/cmr/m /n/10 )]$[][][][][] | [] Overfull \hbox (8.09862pt too wide) in paragraph at lines 37498--37498 []$\OT1/cmr/m/n/10 [[\OT1/cmss/m/n/10 x[]y\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 z\ OT1/cmr/m/n/10 ] [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U \OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\O T1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/ m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/1 0 [[\OT1/cmss/m/n/10 x[]y\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 z\OT1/cmr/m/n/10 ] [] [\OT1/cmss/m/n/10 x[]y\OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 z \OMS/cmsy/m/n/10 `| [] [113] [114] Overfull \hbox (35.33675pt too wide) in paragraph at lines 38679--38679 []$\OT1/cmr/m/n/10 [Re^^Mexivity [] \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 T[] \OMS/ cmsy/m/n/10 ` 8[]\OT1/cmr/m/n/10 : HeadPair[][][][][][][][] [] [] [] []; Transi tivity[][][][][][][][] [] [] [] [][][] [] [] [] [][][][][]\OMS/cmsy/m/n/10 e\OT 1/cmr/m/n/10 ]$ | [] Overfull \hbox (73.50342pt too wide) in paragraph at lines 38778--38778 []$\OT1/cmr/m/n/10 [Commutativity [] \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 T[] \OMS /cmsy/m/n/10 ` 8[]\OT1/cmr/m/n/10 : \OMS/cmsy/m/n/10 8[]\OT1/cmr/m/n/10 : [] = [] \OMS/cmsy/m/n/10 ` \OT1/cmr/m/n/10 Re^^Mexivity[][][][][][][][] [] []; Trans itivity[][][][][][][][] [] [] [] [] [] [][][][][]\OMS/cmsy/m/n/10 e\OT1/cmr/m/n /10 ]$ | [] [115] [116] [117] [118] [119] [120] Overfull \hbox (83.24484pt too wide) in paragraph at lines 42117--42117 \OT1/cmr/m/n/10 conclude[](\OT1/cmss/m/n/10 a[]\OT1/cmr/m/n/10 (conclude[](\OT1 /cmss/m/n/10 a[][][][][][][][]\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 d[][][][]\OT1 /cmr/m/n/10 ))\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmr/ m/n/10 parm(\OT1/cmss/m/n/10 d[][][][]\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 T\OML /cmm/m/it/10 ; \OT1/cmr/m/n/10 1)\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 T\OT1/cmr/ m/n/10 )\OML/cmm/m/it/10 ; []\OT1/cmr/m/n/10 ([]stmt[]\OML/cmm/m/it/10 ; \OT1/c mss/m/n/10 a\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OT1/cmr/m/n/10 ))))))]$[][][] [][] | [] [121] Overfull \hbox (63.1191pt too wide) in paragraph at lines 43155--43155 []$\OT1/cmr/m/n/10 [\OT1/cmss/m/n/10 t[]s \OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 p [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr/m/n/10 (\O T1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/10 ; \OT1/cm ss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [\OT1/cmss/m/n/ 10 t[]s \OT1/cmr/m/n/10 : \OT1/cmss/m/n/10 p [] \OT1/cmr/m/n/10 [[]\OT1/cmss/m/ n/10 s\OT1/cmr/m/n/10 : \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 x\OML/cmm/m/it/10 :\OMS/cmsy/m/n/10 P\OT1/cmr/m/n/10 (\OMS /cmsy/m/n/10 d\OT1/cmss/m/n/10 t \OMS/cmsy/m/n/10 `| [] Overfull \hbox (27.71718pt too wide) in paragraph at lines 43992--43992 []$\OT1/cmr/m/n/10 [Line \OT1/cmss/m/n/10 l \OT1/cmr/m/n/10 : [] \OMS/cmsy/m/n/ 10 ^^] \OT1/cmss/m/n/10 i\OT1/cmr/m/n/10 ; \OT1/cmss/m/n/10 p [] \OML/cmm/m/it/ 10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/it/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\ OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/c mm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1/cmr/m/n/10 [Line \OT1/cmss/m/n/10 l \OT1/cm r/m/n/10 : [] \OMS/cmsy/m/n/10 ^^]| [] Overfull \hbox (4.00888pt too wide) in paragraph at lines 44185--44185 []$\OT1/cmr/m/n/10 [Arbitrary \OMS/cmsy/m/n/10 ^^] \OT1/cmss/m/n/10 i\OT1/cmr/m /n/10 ; \OT1/cmss/m/n/10 p [] \OML/cmm/m/it/10 ^^U\OT1/cmss/m/n/10 t\OML/cmm/m/ it/10 :^^U\OT1/cmss/m/n/10 s\OML/cmm/m/it/10 :^^U\OT1/cmss/m/n/10 c\OML/cmm/m/i t/10 :[]\OT1/cmr/m/n/10 (\OT1/cmss/m/n/10 t\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 s\OML/cmm/m/it/10 ; \OT1/cmss/m/n/10 c\OML/cmm/m/it/10 ; \OMS/cmsy/m/n/10 d\OT1 /cmr/m/n/10 [Arbitrary \OMS/cmsy/m/n/10 ^^] \OT1/cmss/m/n/10 i\OT1/cmr/m/n/10 ; \OT1/cmss/m/n/10 p [] \OT1/cmr/m/n/10 (\OMS/cmsy/m/n/10 8\OT1/cmss/m/n/10 i\OT 1/cmr/m/n/10 : \OT1/cmss/m/n/10 p\OT1/cmr/m/n/10 )]\OMS/cmsy/m/n/10 e\OT1/cmr/m /n/10 )]$[][][][][] | [] [122] [123] [124] [125] [126] (./page.otx [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144] [145] [146] [147] [148] [149] [150] [151] [152] [153] [154]) [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168] [169] [170] [171] [172] [173] [174] [175] [176] [177] [178] (./page.tst [179] [180] [181] [182] [183] [184] [185]) [186] [187] [188] (./page.ind [189] [190] [191] [192] [193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203]) (./page.bbl) [204] (./page.aux) ) Here is how much of TeX's memory you used: 2299 strings out of 95835 31958 string characters out of 1195527 131961 words of memory out of 1000001 5217 multiletter control sequences out of 10000+50000 12259 words of font info for 47 fonts, out of 500000 for 1000 14 hyphenation exceptions out of 1000 25i,27n,37p,6326b,468s stack positions out of 1500i,500n,5000p,200000b,5000s Output written on page.dvi (204 pages, 1071800 bytes).