:: SPRECT_5 semantic presentation begin theorem :: SPRECT_5:1 (Bool "for" (Set (Var "D")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "f")) "being" ($#m2_finseq_1 :::"FinSequence"::: ) "of" (Set (Var "D")) (Bool "for" (Set (Var "q")) "," (Set (Var "p")) "being" ($#m1_subset_1 :::"Element"::: ) "of" (Set (Var "D")) "st" (Bool (Bool (Set (Var "q")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set "(" (Set (Var "f")) ($#k17_finseq_1 :::"|"::: ) (Set "(" (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")) ")" ) ")" )))) "holds" (Bool (Set (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<="::: ) (Set (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))))) ; theorem :: SPRECT_5:2 (Bool "for" (Set (Var "D")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "f")) "being" ($#m2_finseq_1 :::"FinSequence"::: ) "of" (Set (Var "D")) (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "being" ($#m1_subset_1 :::"Element"::: ) "of" (Set (Var "D")) "st" (Bool (Bool (Set (Var "p")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "q")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<="::: ) (Set (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set "(" (Set (Var "f")) ($#k2_finseq_5 :::":-"::: ) (Set (Var "p")) ")" )) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set "(" (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")) ")" ) ($#k6_xcmplx_0 :::"-"::: ) (Set "(" (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")) ")" ) ")" ) ($#k2_xcmplx_0 :::"+"::: ) (Num 1)))))) ; theorem :: SPRECT_5:3 (Bool "for" (Set (Var "D")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "f")) "being" ($#m2_finseq_1 :::"FinSequence"::: ) "of" (Set (Var "D")) (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "being" ($#m1_subset_1 :::"Element"::: ) "of" (Set (Var "D")) "st" (Bool (Bool (Set (Var "p")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "q")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<="::: ) (Set (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set "(" (Set (Var "f")) ($#k1_finseq_5 :::"-:"::: ) (Set (Var "q")) ")" )) ($#r1_hidden :::"="::: ) (Set (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))))) ; theorem :: SPRECT_5:4 (Bool "for" (Set (Var "D")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "f")) "being" ($#m2_finseq_1 :::"FinSequence"::: ) "of" (Set (Var "D")) (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "being" ($#m1_subset_1 :::"Element"::: ) "of" (Set (Var "D")) "st" (Bool (Bool (Set (Var "p")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "q")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<="::: ) (Set (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p")) ")" ")" )) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set "(" (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")) ")" ) ($#k6_xcmplx_0 :::"-"::: ) (Set "(" (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")) ")" ) ")" ) ($#k2_xcmplx_0 :::"+"::: ) (Num 1)))))) ; theorem :: SPRECT_5:5 (Bool "for" (Set (Var "D")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "f")) "being" ($#m2_finseq_1 :::"FinSequence"::: ) "of" (Set (Var "D")) (Bool "for" (Set (Var "p1")) "," (Set (Var "p2")) "," (Set (Var "p3")) "being" ($#m1_subset_1 :::"Element"::: ) "of" (Set (Var "D")) "st" (Bool (Bool (Set (Var "p1")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p2")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p3")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p1")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<="::: ) (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p3")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p1")) ")" ")" )) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p3")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p1")) ")" ")" )))))) ; theorem :: SPRECT_5:6 (Bool "for" (Set (Var "D")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "f")) "being" ($#m2_finseq_1 :::"FinSequence"::: ) "of" (Set (Var "D")) (Bool "for" (Set (Var "p1")) "," (Set (Var "p2")) "," (Set (Var "p3")) "being" ($#m1_subset_1 :::"Element"::: ) "of" (Set (Var "D")) "st" (Bool (Bool (Set (Var "p1")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p2")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p3")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p1")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<="::: ) (Set (Set (Var "p3")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p1")) ")" ")" )) ($#r1_xxreal_0 :::"<="::: ) (Set (Set (Var "p3")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p1")) ")" ")" )))))) ; theorem :: SPRECT_5:7 (Bool "for" (Set (Var "D")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "g")) "being" ($#v1_finseq_6 :::"circular"::: ) ($#m2_finseq_1 :::"FinSequence"::: ) "of" (Set (Var "D")) (Bool "for" (Set (Var "p")) "being" ($#m1_subset_1 :::"Element"::: ) "of" (Set (Var "D")) "st" (Bool (Bool (Set (Var "p")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "g")))) & (Bool (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "g"))) ($#r1_xxreal_0 :::">"::: ) (Num 1))) "holds" (Bool (Set (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "g"))) ($#r1_xxreal_0 :::"<"::: ) (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "g"))))))) ; begin registrationlet "f" be ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::); cluster (Set "f" ($#k1_rfinseq :::"/^"::: ) (Num 1)) -> ($#v2_funct_1 :::"one-to-one"::: ) ; end; theorem :: SPRECT_5:8 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) (Bool "for" (Set (Var "q")) "being" ($#m1_subset_1 :::"Point":::) "of" (Set "(" ($#k15_euclid :::"TOP-REAL"::: ) (Num 2) ")" ) "st" (Bool (Bool (Num 1) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")))) & (Bool (Set (Var "q")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set "(" (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1) ")" ) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "q")) ")" ")" )) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set "(" ($#k3_finseq_1 :::"len"::: ) (Set (Var "f")) ")" ) ($#k2_nat_1 :::"+"::: ) (Num 1) ")" ) ($#k6_xcmplx_0 :::"-"::: ) (Set "(" (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")) ")" ))))) ; theorem :: SPRECT_5:9 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "being" ($#m1_subset_1 :::"Point":::) "of" (Set "(" ($#k15_euclid :::"TOP-REAL"::: ) (Num 2) ")" ) "st" (Bool (Bool (Set (Var "p")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "q")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "q")) ")" ")" )) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set "(" ($#k3_finseq_1 :::"len"::: ) (Set (Var "f")) ")" ) ($#k2_nat_1 :::"+"::: ) (Set "(" (Set (Var "p")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")) ")" ) ")" ) ($#k6_xcmplx_0 :::"-"::: ) (Set "(" (Set (Var "q")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")) ")" ))))) ; theorem :: SPRECT_5:10 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) (Bool "for" (Set (Var "p1")) "," (Set (Var "p2")) "," (Set (Var "p3")) "being" ($#m1_subset_1 :::"Point":::) "of" (Set "(" ($#k15_euclid :::"TOP-REAL"::: ) (Num 2) ")" ) "st" (Bool (Bool (Set (Var "p1")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p2")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p3")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p1")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p3")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set (Var "p3")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p2")) ")" ")" )) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p1")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p2")) ")" ")" ))))) ; theorem :: SPRECT_5:11 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) (Bool "for" (Set (Var "p1")) "," (Set (Var "p2")) "," (Set (Var "p3")) "being" ($#m1_subset_1 :::"Point":::) "of" (Set "(" ($#k15_euclid :::"TOP-REAL"::: ) (Num 2) ")" ) "st" (Bool (Bool (Set (Var "p1")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p2")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p3")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p1")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p3")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set (Var "p1")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p3")) ")" ")" )) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p3")) ")" ")" ))))) ; theorem :: SPRECT_5:12 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) (Bool "for" (Set (Var "p1")) "," (Set (Var "p2")) "," (Set (Var "p3")) "being" ($#m1_subset_1 :::"Point":::) "of" (Set "(" ($#k15_euclid :::"TOP-REAL"::: ) (Num 2) ")" ) "st" (Bool (Bool (Set (Var "p1")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p2")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Var "p3")) ($#r2_hidden :::"in"::: ) (Set ($#k10_xtuple_0 :::"rng"::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p1")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<="::: ) (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f")))) & (Bool (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set (Var "p3")) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) "holds" (Bool (Set (Set (Var "p1")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p3")) ")" ")" )) ($#r1_xxreal_0 :::"<="::: ) (Set (Set (Var "p2")) ($#k4_finseq_4 :::".."::: ) (Set "(" ($#k1_finseq_6 :::"Rotate"::: ) "(" (Set (Var "f")) "," (Set (Var "p3")) ")" ")" ))))) ; theorem :: SPRECT_5:13 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "holds" (Bool (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:14 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "holds" (Bool (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:15 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "holds" (Bool (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:16 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "holds" (Bool (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:17 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "holds" (Bool (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:18 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "holds" (Bool (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:19 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "holds" (Bool (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:20 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "holds" (Bool (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set ($#k3_finseq_1 :::"len"::: ) (Set (Var "f"))))) ; begin theorem :: SPRECT_5:21 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:22 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::">"::: ) (Num 1))) ; theorem :: SPRECT_5:23 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:24 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:25 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:26 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:27 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:28 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:29 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:30 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::">"::: ) (Num 1))) ; theorem :: SPRECT_5:31 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:32 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:33 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:34 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:35 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:36 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:37 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:38 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::">"::: ) (Num 1))) ; theorem :: SPRECT_5:39 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:40 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:41 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:42 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:43 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:44 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:45 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ))) & (Bool (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:46 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:47 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:48 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:49 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:50 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:51 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:52 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ))) & (Bool (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:53 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:54 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:55 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:56 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:57 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:58 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:59 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ))) & (Bool (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:60 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:61 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:62 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:63 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:64 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:65 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:66 (Bool "for" (Set (Var "f")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "f")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ))) & (Bool (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" )))) "holds" (Bool (Set (Set "(" ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "f")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "f"))))) ; theorem :: SPRECT_5:67 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k20_pscomp_1 :::"N-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:68 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k21_pscomp_1 :::"N-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:69 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k22_pscomp_1 :::"E-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:70 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k23_pscomp_1 :::"E-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:71 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k24_pscomp_1 :::"S-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ; theorem :: SPRECT_5:72 (Bool "for" (Set (Var "z")) "being" ($#~v3_funct_1 "non" ($#v3_funct_1 :::"constant"::: ) ) ($#v2_goboard5 :::"standard"::: ) ($#v1_sprect_2 :::"clockwise_oriented"::: ) ($#m2_finseq_1 :::"special_circular_sequence":::) "st" (Bool (Bool (Set (Set (Var "z")) ($#k7_partfun1 :::"/."::: ) (Num 1)) ($#r1_hidden :::"="::: ) (Set ($#k19_pscomp_1 :::"W-max"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ))) & (Bool (Set ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )) ($#r1_hidden :::"<>"::: ) (Set ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" )))) "holds" (Bool (Set (Set "(" ($#k25_pscomp_1 :::"S-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))) ($#r1_xxreal_0 :::"<"::: ) (Set (Set "(" ($#k18_pscomp_1 :::"W-min"::: ) (Set "(" ($#k3_topreal1 :::"L~"::: ) (Set (Var "z")) ")" ) ")" ) ($#k4_finseq_4 :::".."::: ) (Set (Var "z"))))) ;