:: BVFUNC10  semantic presentation begin  



theorem :: BVFUNC10:1 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "c"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "a")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "a")) ")" ))))) ; 
 
theorem :: BVFUNC10:2 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "c"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" ) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "c"))  ($#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 :: BVFUNC10:3 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" ) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#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 :: BVFUNC10:4 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) )  "st" (Bool (Bool (Set (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a")))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")))) & (Bool (Set (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y"))))) "holds"  (Bool (Set (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")))))) ; 
 
theorem :: BVFUNC10:5 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) )  "st" (Bool (Bool (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")))) & (Bool (Set (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y"))))) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")))))) ; 
 
theorem :: BVFUNC10:6 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a1")) "," (Set (Var "a2")) "," (Set (Var "b1")) "," (Set (Var "b2")) "," (Set (Var "c1")) "," (Set (Var "c2")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "a1"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a2")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b1"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c1"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "(" (Set (Var "a1"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b1")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c1")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a2"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b2")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c2")))))) ; 
 
theorem :: BVFUNC10:7 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a1")) "," (Set (Var "a2")) "," (Set (Var "b1")) "," (Set (Var "b2")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "a1"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b1")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a2"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a1"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "a2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "b1"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b2")) ")" ) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "b1"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a1")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b2"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b1"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a1"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "a2")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC10:8 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "d")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" ))))) ; 
 
theorem :: BVFUNC10:9 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a1")) "," (Set (Var "a2")) "," (Set (Var "b1")) "," (Set (Var "b2")) "," (Set (Var "b3")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a1"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "a2")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set  "(" (Set (Var "b1"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b2")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b3")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a1"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b1")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a1"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a1"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b3")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a2"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b1")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a2"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a2"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b3")) ")" ))))) ; 
 
theorem :: BVFUNC10:10 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#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 "d")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "c"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ))))) ; 
 
theorem :: BVFUNC10:11 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#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 "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "d")))))) ; 
 
theorem :: BVFUNC10:12 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "a")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")))))) ; 
 
theorem :: BVFUNC10:13 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a1")) "," (Set (Var "a2")) "," (Set (Var "a3")) "," (Set (Var "b1")) "," (Set (Var "b2")) "," (Set (Var "b3")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set (Var "a1"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "a2")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "a3")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set  "(" (Set (Var "b1"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b2")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b3")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b1")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "a3")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a1")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a2")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b3")) ")" ))))) ; 
 
theorem :: BVFUNC10:14 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#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")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (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  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC10:15 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#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")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")))))) ; 
 
theorem :: BVFUNC10:16 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "a")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" ) ")" ))  ($#r2_funct_2 :::"="::: )  (Set (Set  "(" (Set  "(" (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (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  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC10:17 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" ))))) ; 
 
theorem :: BVFUNC10:18 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")))))) ; 
 
theorem :: BVFUNC10:19 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" ))))) ; 
 
theorem :: BVFUNC10:20 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC10:21 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "a")) ")" ))))) ; 
 
theorem :: BVFUNC10:22 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC10:23 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "a")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC10:24 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))))) ; 
 
theorem :: BVFUNC10:25 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "a")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC10:26 (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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "a")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC10:27 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "c"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" ) ")" ) ")" ))))) ;