:: BVFUNC26 semantic presentation begin definitionlet "p", "q" be ($#v1_margrel1 :::"boolean-valued"::: ) ($#m1_hidden :::"Function":::); func "p" :::"'nand'"::: "q" -> ($#m1_hidden :::"Function":::) means :: BVFUNC26:def 1 (Bool "(" (Bool (Set ($#k9_xtuple_0 :::"dom"::: ) it) ($#r1_hidden :::"="::: ) (Set (Set "(" ($#k9_xtuple_0 :::"dom"::: ) "p" ")" ) ($#k3_xboole_0 :::"/\"::: ) (Set "(" ($#k9_xtuple_0 :::"dom"::: ) "q" ")" ))) & (Bool "(" "for" (Set (Var "x")) "being" ($#m1_hidden :::"set"::: ) "st" (Bool (Bool (Set (Var "x")) ($#r2_hidden :::"in"::: ) (Set ($#k9_xtuple_0 :::"dom"::: ) it))) "holds" (Bool (Set it ($#k1_funct_1 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" "p" ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ) ($#k8_xboolean :::"'nand'"::: ) (Set "(" "q" ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ))) ")" ) ")" ); commutativity (Bool "for" (Set (Var "b1")) "being" ($#m1_hidden :::"Function":::) (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "being" ($#v1_margrel1 :::"boolean-valued"::: ) ($#m1_hidden :::"Function":::) "st" (Bool (Bool (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b1"))) ($#r1_hidden :::"="::: ) (Set (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "p")) ")" ) ($#k3_xboole_0 :::"/\"::: ) (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "q")) ")" ))) & (Bool "(" "for" (Set (Var "x")) "being" ($#m1_hidden :::"set"::: ) "st" (Bool (Bool (Set (Var "x")) ($#r2_hidden :::"in"::: ) (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b1"))))) "holds" (Bool (Set (Set (Var "b1")) ($#k1_funct_1 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set (Var "p")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ) ($#k8_xboolean :::"'nand'"::: ) (Set "(" (Set (Var "q")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ))) ")" )) "holds" (Bool "(" (Bool (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b1"))) ($#r1_hidden :::"="::: ) (Set (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "q")) ")" ) ($#k3_xboole_0 :::"/\"::: ) (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "p")) ")" ))) & (Bool "(" "for" (Set (Var "x")) "being" ($#m1_hidden :::"set"::: ) "st" (Bool (Bool (Set (Var "x")) ($#r2_hidden :::"in"::: ) (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b1"))))) "holds" (Bool (Set (Set (Var "b1")) ($#k1_funct_1 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set (Var "q")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ) ($#k8_xboolean :::"'nand'"::: ) (Set "(" (Set (Var "p")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ))) ")" ) ")" ))) ; func "p" :::"'nor'"::: "q" -> ($#m1_hidden :::"Function":::) means :: BVFUNC26:def 2 (Bool "(" (Bool (Set ($#k9_xtuple_0 :::"dom"::: ) it) ($#r1_hidden :::"="::: ) (Set (Set "(" ($#k9_xtuple_0 :::"dom"::: ) "p" ")" ) ($#k3_xboole_0 :::"/\"::: ) (Set "(" ($#k9_xtuple_0 :::"dom"::: ) "q" ")" ))) & (Bool "(" "for" (Set (Var "x")) "being" ($#m1_hidden :::"set"::: ) "st" (Bool (Bool (Set (Var "x")) ($#r2_hidden :::"in"::: ) (Set ($#k9_xtuple_0 :::"dom"::: ) it))) "holds" (Bool (Set it ($#k1_funct_1 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" "p" ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ) ($#k9_xboolean :::"'nor'"::: ) (Set "(" "q" ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ))) ")" ) ")" ); commutativity (Bool "for" (Set (Var "b1")) "being" ($#m1_hidden :::"Function":::) (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "being" ($#v1_margrel1 :::"boolean-valued"::: ) ($#m1_hidden :::"Function":::) "st" (Bool (Bool (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b1"))) ($#r1_hidden :::"="::: ) (Set (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "p")) ")" ) ($#k3_xboole_0 :::"/\"::: ) (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "q")) ")" ))) & (Bool "(" "for" (Set (Var "x")) "being" ($#m1_hidden :::"set"::: ) "st" (Bool (Bool (Set (Var "x")) ($#r2_hidden :::"in"::: ) (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b1"))))) "holds" (Bool (Set (Set (Var "b1")) ($#k1_funct_1 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set (Var "p")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ) ($#k9_xboolean :::"'nor'"::: ) (Set "(" (Set (Var "q")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ))) ")" )) "holds" (Bool "(" (Bool (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b1"))) ($#r1_hidden :::"="::: ) (Set (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "q")) ")" ) ($#k3_xboole_0 :::"/\"::: ) (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "p")) ")" ))) & (Bool "(" "for" (Set (Var "x")) "being" ($#m1_hidden :::"set"::: ) "st" (Bool (Bool (Set (Var "x")) ($#r2_hidden :::"in"::: ) (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b1"))))) "holds" (Bool (Set (Set (Var "b1")) ($#k1_funct_1 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set (Var "q")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ) ($#k9_xboolean :::"'nor'"::: ) (Set "(" (Set (Var "p")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ))) ")" ) ")" ))) ; end; :: deftheorem defines :::"'nand'"::: BVFUNC26:def 1 : (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "being" ($#v1_margrel1 :::"boolean-valued"::: ) ($#m1_hidden :::"Function":::) (Bool "for" (Set (Var "b3")) "being" ($#m1_hidden :::"Function":::) "holds" (Bool "(" (Bool (Set (Var "b3")) ($#r1_hidden :::"="::: ) (Set (Set (Var "p")) ($#k1_bvfunc26 :::"'nand'"::: ) (Set (Var "q")))) "iff" (Bool "(" (Bool (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b3"))) ($#r1_hidden :::"="::: ) (Set (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "p")) ")" ) ($#k3_xboole_0 :::"/\"::: ) (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "q")) ")" ))) & (Bool "(" "for" (Set (Var "x")) "being" ($#m1_hidden :::"set"::: ) "st" (Bool (Bool (Set (Var "x")) ($#r2_hidden :::"in"::: ) (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b3"))))) "holds" (Bool (Set (Set (Var "b3")) ($#k1_funct_1 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set (Var "p")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ) ($#k8_xboolean :::"'nand'"::: ) (Set "(" (Set (Var "q")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ))) ")" ) ")" ) ")" ))); :: deftheorem defines :::"'nor'"::: BVFUNC26:def 2 : (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "being" ($#v1_margrel1 :::"boolean-valued"::: ) ($#m1_hidden :::"Function":::) (Bool "for" (Set (Var "b3")) "being" ($#m1_hidden :::"Function":::) "holds" (Bool "(" (Bool (Set (Var "b3")) ($#r1_hidden :::"="::: ) (Set (Set (Var "p")) ($#k2_bvfunc26 :::"'nor'"::: ) (Set (Var "q")))) "iff" (Bool "(" (Bool (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b3"))) ($#r1_hidden :::"="::: ) (Set (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "p")) ")" ) ($#k3_xboole_0 :::"/\"::: ) (Set "(" ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "q")) ")" ))) & (Bool "(" "for" (Set (Var "x")) "being" ($#m1_hidden :::"set"::: ) "st" (Bool (Bool (Set (Var "x")) ($#r2_hidden :::"in"::: ) (Set ($#k9_xtuple_0 :::"dom"::: ) (Set (Var "b3"))))) "holds" (Bool (Set (Set (Var "b3")) ($#k1_funct_1 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set (Var "p")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ) ($#k9_xboolean :::"'nor'"::: ) (Set "(" (Set (Var "q")) ($#k1_funct_1 :::"."::: ) (Set (Var "x")) ")" ))) ")" ) ")" ) ")" ))); registrationlet "p", "q" be ($#v1_margrel1 :::"boolean-valued"::: ) ($#m1_hidden :::"Function":::); cluster (Set "p" ($#k1_bvfunc26 :::"'nand'"::: ) "q") -> ($#v1_margrel1 :::"boolean-valued"::: ) ; cluster (Set "p" ($#k2_bvfunc26 :::"'nor'"::: ) "q") -> ($#v1_margrel1 :::"boolean-valued"::: ) ; end; definitionlet "A" be ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) ; let "p", "q" be ($#m1_subset_1 :::"Function":::) "of" (Set (Const "A")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ); :: original: :::"'nand'"::: redefine func "p" :::"'nand'"::: "q" -> ($#m1_subset_1 :::"Function":::) "of" "A" "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) means :: BVFUNC26:def 3 (Bool "for" (Set (Var "x")) "being" ($#m1_subset_1 :::"Element"::: ) "of" "A" "holds" (Bool (Set it ($#k3_funct_2 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" "p" ($#k3_funct_2 :::"."::: ) (Set (Var "x")) ")" ) ($#k19_bvfunc_1 :::"'nand'"::: ) (Set "(" "q" ($#k3_funct_2 :::"."::: ) (Set (Var "x")) ")" )))); :: original: :::"'nor'"::: redefine func "p" :::"'nor'"::: "q" -> ($#m1_subset_1 :::"Function":::) "of" "A" "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) means :: BVFUNC26:def 4 (Bool "for" (Set (Var "x")) "being" ($#m1_subset_1 :::"Element"::: ) "of" "A" "holds" (Bool (Set it ($#k3_funct_2 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" "p" ($#k3_funct_2 :::"."::: ) (Set (Var "x")) ")" ) ($#k20_bvfunc_1 :::"'nor'"::: ) (Set "(" "q" ($#k3_funct_2 :::"."::: ) (Set (Var "x")) ")" )))); end; :: deftheorem defines :::"'nand'"::: BVFUNC26:def 3 : (Bool "for" (Set (Var "A")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "," (Set (Var "b4")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "A")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Var "b4")) ($#r1_hidden :::"="::: ) (Set (Set (Var "p")) ($#k3_bvfunc26 :::"'nand'"::: ) (Set (Var "q")))) "iff" (Bool "for" (Set (Var "x")) "being" ($#m1_subset_1 :::"Element"::: ) "of" (Set (Var "A")) "holds" (Bool (Set (Set (Var "b4")) ($#k3_funct_2 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set (Var "p")) ($#k3_funct_2 :::"."::: ) (Set (Var "x")) ")" ) ($#k19_bvfunc_1 :::"'nand'"::: ) (Set "(" (Set (Var "q")) ($#k3_funct_2 :::"."::: ) (Set (Var "x")) ")" )))) ")" ))); :: deftheorem defines :::"'nor'"::: BVFUNC26:def 4 : (Bool "for" (Set (Var "A")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "p")) "," (Set (Var "q")) "," (Set (Var "b4")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "A")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Var "b4")) ($#r1_hidden :::"="::: ) (Set (Set (Var "p")) ($#k4_bvfunc26 :::"'nor'"::: ) (Set (Var "q")))) "iff" (Bool "for" (Set (Var "x")) "being" ($#m1_subset_1 :::"Element"::: ) "of" (Set (Var "A")) "holds" (Bool (Set (Set (Var "b4")) ($#k3_funct_2 :::"."::: ) (Set (Var "x"))) ($#r1_hidden :::"="::: ) (Set (Set "(" (Set (Var "p")) ($#k3_funct_2 :::"."::: ) (Set (Var "x")) ")" ) ($#k20_bvfunc_1 :::"'nor'"::: ) (Set "(" (Set (Var "q")) ($#k3_funct_2 :::"."::: ) (Set (Var "x")) ")" )))) ")" ))); definitionlet "Y" be ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) ; let "a", "b" be ($#m1_subset_1 :::"Function":::) "of" (Set (Const "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ); :: original: :::"'nand'"::: redefine func "a" :::"'nand'"::: "b" -> ($#m1_subset_1 :::"Function":::) "of" "Y" "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ); :: original: :::"'nor'"::: redefine func "a" :::"'nor'"::: "b" -> ($#m1_subset_1 :::"Function":::) "of" "Y" "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ); end; theorem :: BVFUNC26:1 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b"))) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:2 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b"))) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:3 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" ) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "a"))) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")))))) ; theorem :: BVFUNC26:4 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" ) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "a"))) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))))) ; theorem :: BVFUNC26:5 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) "holds" (Bool "(" (Bool (Set (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" ) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))) & (Bool (Set (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" ) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))) & (Bool (Set (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" ) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))) ")" )) ; theorem :: BVFUNC26:6 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "a"))) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")))) & (Bool (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "a")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Var "a"))) ")" ))) ; theorem :: BVFUNC26:7 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")))))) ; theorem :: BVFUNC26:8 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))) & (Bool (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))) ")" ))) ; theorem :: BVFUNC26:9 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:10 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")))))) ; theorem :: BVFUNC26:11 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ) ")" ))))) ; theorem :: BVFUNC26:12 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc_1 :::"'xor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:13 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" (Set (Var "b")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ))) & (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set "(" (Set (Var "b")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ))) ")" ))) ; theorem :: BVFUNC26:14 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")))) & (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ))) ")" ))) ; theorem :: BVFUNC26:15 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc_1 :::"'xor'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:16 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")))))) ; theorem :: BVFUNC26:17 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ")" ))))) ; theorem :: BVFUNC26:18 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc_1 :::"'xor'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:19 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")))) & (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set (Var "b")))) ")" ))) ; theorem :: BVFUNC26:20 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))))) ; theorem :: BVFUNC26:21 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:22 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b"))) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" ) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:23 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" ) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:24 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ) ")" ))))) ; theorem :: BVFUNC26:25 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:26 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" ) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "a"))) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))))) ; theorem :: BVFUNC26:27 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" ) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "a"))) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")))))) ; theorem :: BVFUNC26:28 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) "holds" (Bool "(" (Bool (Set (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" ) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))) & (Bool (Set (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" ) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))) & (Bool (Set (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" ) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))) ")" )) ; theorem :: BVFUNC26:29 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "a"))) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")))) & (Bool (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "a")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Var "a"))) ")" ))) ; theorem :: BVFUNC26:30 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")))))) ; theorem :: BVFUNC26:31 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))) & (Bool (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))) ")" ))) ; theorem :: BVFUNC26:32 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc_1 :::"'xor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")))))) ; theorem :: BVFUNC26:33 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "b")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ) ")" ))))) ; theorem :: BVFUNC26:34 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:35 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "b")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc_1 :::"'xor'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:36 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "b")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:37 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")))))) ; theorem :: BVFUNC26:38 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:39 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ) ")" ))))) ; theorem :: BVFUNC26:40 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:41 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")))))) ; theorem :: BVFUNC26:42 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))))) ; theorem :: BVFUNC26:43 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))))) ; theorem :: BVFUNC26:44 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")))))) ; theorem :: BVFUNC26:45 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) "holds" (Bool (Set (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" ) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y"))))) ; theorem :: BVFUNC26:46 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) "holds" (Bool (Set (Set "(" ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")) ")" ) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y"))))) ; theorem :: BVFUNC26:47 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) "holds" (Bool (Set (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" ) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set "(" ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y"))))) ; theorem :: BVFUNC26:48 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool "(" (Bool (Set (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set (Var "a"))) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))) & (Bool (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set (Var "a")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))) ")" ))) ; theorem :: BVFUNC26:49 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:50 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "c")) ")" ) ")" ))))) ; theorem :: BVFUNC26:51 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:52 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc_1 :::"'xor'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "b")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ) ")" ) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:53 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "b")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ) ")" ) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" (Set "(" (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:54 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:55 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "c")) ")" ) ")" ))))) ; theorem :: BVFUNC26:56 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:57 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))))) ; theorem :: BVFUNC26:58 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc_1 :::"'xor'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")))))) ; theorem :: BVFUNC26:59 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:60 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:61 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))))) ; theorem :: BVFUNC26:62 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:63 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "c")) ")" ) ")" ))))) ; theorem :: BVFUNC26:64 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc_1 :::"'xor'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ) ")" ) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set "(" (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ))))) ; theorem :: BVFUNC26:65 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ) ")" ) ")" ))))) ; theorem :: BVFUNC26:66 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "b")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")) ")" ) ")" ))))) ; theorem :: BVFUNC26:67 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "b")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "c")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "b")) ")" ) ($#k5_bvfunc_1 :::"'or'"::: ) (Set (Var "c")))))) ; theorem :: BVFUNC26:68 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k11_bvfunc_1 :::"O_el"::: ) (Set (Var "Y")))))) ; theorem :: BVFUNC26:69 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:70 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k6_bvfunc_1 :::"'xor'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "b")) ")" ))))) ; theorem :: BVFUNC26:71 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k10_bvfunc_1 :::"'eqv'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set (Set "(" ($#k1_bvfunc_1 :::"'not'"::: ) (Set (Var "a")) ")" ) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")))))) ; theorem :: BVFUNC26:72 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k9_bvfunc_1 :::"'imp'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k1_bvfunc_1 :::"'not'"::: ) (Set "(" (Set (Var "a")) ($#k5_bvfunc_1 :::"'or'"::: ) (Set "(" (Set (Var "a")) ($#k2_bvfunc_1 :::"'&'"::: ) (Set (Var "b")) ")" ) ")" ))))) ; theorem :: BVFUNC26:73 (Bool "for" (Set (Var "Y")) "being" ($#~v1_xboole_0 "non" ($#v1_xboole_0 :::"empty"::: ) ) ($#m1_hidden :::"set"::: ) (Bool "for" (Set (Var "a")) "," (Set (Var "b")) "being" ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds" (Bool (Set (Set (Var "a")) ($#k5_bvfunc26 :::"'nand'"::: ) (Set "(" (Set (Var "a")) ($#k6_bvfunc26 :::"'nor'"::: ) (Set (Var "b")) ")" )) ($#r2_funct_2 :::"="::: ) (Set ($#k12_bvfunc_1 :::"I_el"::: ) (Set (Var "Y")))))) ;