:: BVFUNC_8  semantic presentation begin  



theorem :: BVFUNC_8:1 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ))))) ; 
 
theorem :: BVFUNC_8:2 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "d")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ))))) ; 
 
theorem :: BVFUNC_8:3 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ))))) ; 
 
theorem :: BVFUNC_8:4 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ))))) ; 
 
theorem :: BVFUNC_8:5 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))))) ; 
 
theorem :: BVFUNC_8:6 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Var "a"))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC_8:7 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Var "a"))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC_8:8 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Var "a"))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC_8:9 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Var "a"))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#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 :: BVFUNC_8:10 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")))  ($#r2_funct_2 :::"="::: )  (Set (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" ))))) ; 
 
theorem :: BVFUNC_8:11 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")))  ($#r2_funct_2 :::"="::: )  (Set (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" ))))) ; 
 
theorem :: BVFUNC_8:12 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k6_bvfunc_1 :::"'xor'"::: )  (Set (Var "b")))  ($#r2_funct_2 :::"="::: )  (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a"))  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set (Var "b")) ")" ))))) ; 
 
theorem :: BVFUNC_8:13 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k6_bvfunc_1 :::"'xor'"::: )  (Set (Var "b")))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC_8:14 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k6_bvfunc_1 :::"'xor'"::: )  (Set  "("  ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")))))) ; 
 
theorem :: BVFUNC_8:15 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k6_bvfunc_1 :::"'xor'"::: )  (Set  "("  ($#k11_bvfunc_1 :::"O_el"::: )  (Set (Var "Y")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Var "a"))))) ; 
 
theorem :: BVFUNC_8:16 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k6_bvfunc_1 :::"'xor'"::: )  (Set (Var "b")))  ($#r2_funct_2 :::"="::: )  (Set (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k6_bvfunc_1 :::"'xor'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ))))) ; 
 
theorem :: BVFUNC_8:17 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a"))  ($#k6_bvfunc_1 :::"'xor'"::: )  (Set (Var "b")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set (Var "a"))  ($#k6_bvfunc_1 :::"'xor'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ))))) ; 
 
theorem :: BVFUNC_8:18 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set (Var "b")))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" ))))) ; 
 
theorem :: BVFUNC_8:19 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set (Var "b")))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC_8:20 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set  "("  ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Var "a"))))) ; 
 
theorem :: BVFUNC_8:21 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set  "("  ($#k11_bvfunc_1 :::"O_el"::: )  (Set (Var "Y")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")))))) ; 
 
theorem :: BVFUNC_8:22 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a"))  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set (Var "b")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set (Var "a"))  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ))))) ; 
 
theorem :: BVFUNC_8:23 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" ))))) ; 
 
theorem :: BVFUNC_8:24 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a")) ")" )  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ))))) ; 
 
theorem :: BVFUNC_8:25 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Var "a"))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "a")) ")" ) ")" )  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set (Var "a")))))) ; 
 
theorem :: BVFUNC_8:26 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k10_bvfunc_1 :::"'eqv'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" ) ")" ))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")))))) ; 
 
theorem :: BVFUNC_8:27 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a")))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")))))) ; 
 
theorem :: BVFUNC_8:28 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "d")) ")" ) ")" ) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" ))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")))))) ; 
 
theorem :: BVFUNC_8:29 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ) ")" ))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")))))) ;