:: BVFUNC_9  semantic presentation begin  












theorem :: BVFUNC_9:1 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")))))) ; 
 
theorem :: BVFUNC_9:2 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b"))))) ; 
 
theorem :: BVFUNC_9:3 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")))))) ; 
 
theorem :: BVFUNC_9:4 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b"))))) ; 
 
theorem :: BVFUNC_9:5 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b"))))) ; 
 
theorem :: BVFUNC_9:6 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")) ")" ) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")))))) ; 
 
theorem :: BVFUNC_9:7 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "being"   ($#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"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")))))) ; 
 
theorem :: BVFUNC_9:8 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")))))) ; 
 
theorem :: BVFUNC_9:9 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")))))) ; 
 
theorem :: BVFUNC_9:10 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" ))))) ; 
 
theorem :: BVFUNC_9:11 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" ))))) ; 
 
theorem :: BVFUNC_9:12 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" ))))) ; 
 
theorem :: BVFUNC_9:13 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")))))) ; 
 
theorem :: BVFUNC_9:14 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "c"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")))))) ; 
 
theorem :: BVFUNC_9:15 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")))))) ; 
 
theorem :: BVFUNC_9:16 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")))))) ; 
 
theorem :: BVFUNC_9:17 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "c")) "," (Set (Var "b")) "being"   ($#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 "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ) ")" ))  ($#r1_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_9:18 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "a")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")))))) ; 
 
theorem :: BVFUNC_9:19 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" ))))) ; 
 
theorem :: BVFUNC_9:20 (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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#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 :: BVFUNC_9:21 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "c")) "," (Set (Var "b")) "being"   ($#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 "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#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 :: BVFUNC_9:22 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "d")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "(" (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "d")) ")" ))))) ; 
 
theorem :: BVFUNC_9:23 (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")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#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 :: BVFUNC_9:24 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a1")) "," (Set (Var "b1")) "," (Set (Var "c1")) "," (Set (Var "a2")) "," (Set (Var "b2")) "," (Set (Var "c2")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "b1"))  ($#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")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c1")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a2"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b2")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a2"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c2")) ")" ) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a2"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a1")))))) ; 
 
theorem :: BVFUNC_9:25 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a1")) "," (Set (Var "b1")) "," (Set (Var "c1")) "," (Set (Var "a2")) "," (Set (Var "b2")) "," (Set (Var "c2")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a1"))  ($#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")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c1")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a2"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b2")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a2"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c2")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "b2"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c2")) ")" ) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set  "(" (Set (Var "a2"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "a1")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b2"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b1")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "c2"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c1")) ")" ))))) ; 
 
theorem :: BVFUNC_9:26 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a1")) "," (Set (Var "b1")) "," (Set (Var "a2")) "," (Set (Var "b2")) "being"   ($#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 "a2")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b1"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "b2")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a2"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b2")) ")" ) ")" ) ")" )  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a1"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b1")) ")" ) ")" ))  ($#r2_funct_2 :::"="::: )  (Set   ($#k12_bvfunc_1 :::"I_el"::: )  (Set (Var "Y")))))) ; 
 
theorem :: BVFUNC_9:27 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a1")) "," (Set (Var "b1")) "," (Set (Var "c1")) "," (Set (Var "a2")) "," (Set (Var "b2")) "," (Set (Var "c2")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a1"))  ($#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")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a2"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b2")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a2"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c2")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "b2"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c2")) ")" ) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set  "(" (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a1"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b1")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "a1"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c1")) ")" ) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set  "(" (Set (Var "b1"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c1")) ")" ) ")" ))))) ; 
 
theorem :: BVFUNC_9:28 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "a"))))) ; 
 
theorem :: BVFUNC_9:29 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"   (Bool  "("  (Bool (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "a"))) & (Bool (Set (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b")))  ")" ))) ; 
 
theorem :: BVFUNC_9:30 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"   (Bool  "("  (Bool (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "a"))) & (Bool (Set (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b")))  ")" ))) ; 
 
theorem :: BVFUNC_9:31 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "," (Set (Var "e")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"   (Bool  "("  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "e")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "a"))) & (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "e")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b")))  ")" ))) ; 
 
theorem :: BVFUNC_9:32 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "," (Set (Var "e")) "," (Set (Var "f")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"   (Bool  "("  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "e")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "f")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "a"))) & (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "e")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "f")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b")))  ")" ))) ; 
 
theorem :: BVFUNC_9:33 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "," (Set (Var "e")) "," (Set (Var "f")) "," (Set (Var "g")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"   (Bool  "("  (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "e")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "f")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "g")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "a"))) & (Bool (Set (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "e")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "f")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "g")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b")))  ")" ))) ; 
 
theorem :: BVFUNC_9:34 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) )  "st" (Bool (Bool (Set (Var "a"))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b"))) & (Bool (Set (Var "c"))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "d")))) "holds"  (Bool (Set (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "c")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "b"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "d")))))) ; 
 
theorem :: BVFUNC_9:35 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) )  "st" (Bool (Bool (Set (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "c")))) "holds"  (Bool (Set (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "("  ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "c")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set   ($#k1_bvfunc_1 :::"'not'"::: )  (Set (Var "b")))))) ; 
 
theorem :: BVFUNC_9:36 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "c")) "," (Set (Var "b")) "being"   ($#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 "c")) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "c"))))) ; 
 
theorem :: BVFUNC_9:37 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "c")) "," (Set (Var "b")) "being"   ($#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 "c")) ")" )  ($#k5_bvfunc_1 :::"'or'"::: )  (Set  "(" (Set (Var "b"))  ($#k9_bvfunc_1 :::"'imp'"::: )  (Set (Var "c")) ")" ) ")" )  ($#k2_bvfunc_1 :::"'&'"::: )  (Set  "(" (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")) ")" ))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "c"))))) ; 
 
theorem :: BVFUNC_9:38 (Bool  "for" (Set (Var "Y")) "being"  ($#~v1_xboole_0  "non"   ($#v1_xboole_0 :::"empty"::: )   )    ($#m1_hidden :::"set"::: )    (Bool  "for" (Set (Var "a")) "," (Set (Var "b")) "," (Set (Var "c")) "," (Set (Var "d")) "being"   ($#m1_subset_1 :::"Function":::) "of" (Set (Var "Y")) "," (Set  ($#k6_margrel1 :::"BOOLEAN"::: ) )  "st" (Bool (Bool (Set (Var "a"))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "b"))) & (Bool (Set (Var "c"))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Var "d")))) "holds"  (Bool (Set (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "c")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "b"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "d")))))) ; 
 
theorem :: BVFUNC_9:39 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Var "a"))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")))))) ; 
 
theorem :: BVFUNC_9:40 (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  ($#k6_margrel1 :::"BOOLEAN"::: ) ) "holds"  (Bool (Set (Set (Var "a"))  ($#k2_bvfunc_1 :::"'&'"::: )  (Set (Var "b")))  ($#r1_bvfunc_1 :::"'<'"::: )  (Set (Set (Var "a"))  ($#k5_bvfunc_1 :::"'or'"::: )  (Set (Var "b")))))) ;