include('Axioms/binary_ieee^2.ax').
thf(tp_c_2EHolSmt_2Earray__ext,type,(c_2EHolSmt_2Earray__ext:(del>(del>$i)))).
thf(mem_c_2EHolSmt_2Earray__ext,axiom,( ! [A_27a:del] : ( ! [A_27b:del] : (mem@(c_2EHolSmt_2Earray__ext@A_27a@A_27b)@(arr@(arr@A_27a@A_27b)@(arr@(arr@A_27a@A_27b)@A_27a)))))).
thf(tp_c_2EHolSmt_2Exor,type,(c_2EHolSmt_2Exor:$i)).
thf(mem_c_2EHolSmt_2Exor,axiom,(mem@c_2EHolSmt_2Exor@(arr@bool@(arr@bool@bool)))).
thf(ax_thm_2EHolSmt_2Exor__def,axiom,( ! [V0x:$i] : ((mem@V0x@bool) => ( ! [V1y:$i] : ((mem@V1y@bool) => ((p@(ap@(ap@c_2EHolSmt_2Exor@V0x)@V1y)) <=> (~ ((p@V0x) <=> (p@V1y))))))))).
thf(ax_thm_2EHolSmt_2Earray__ext__def,axiom,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0A:$i] : ((mem@V0A@(arr@A_27a@A_27b)) => ( ! [V1B:$i] : ((mem@V1B@(arr@A_27a@A_27b)) => ((ap@(ap@(c_2EHolSmt_2Earray__ext@A_27a@A_27b)@V0A)@V1B) = (ap@(c_2Emin_2E_40@A_27a)@(lam@A_27a@(^ [V2i:$i] : (ap@c_2Ebool_2E_7E@(ap@(ap@(c_2Emin_2E_3D@A_27b)@(ap@V0A@V2i))@(ap@V1B@V2i)))))))))))))).
thf(conj_thm_2EHolSmt_2EALL__DISTINCT__NIL,lemma,( ! [A_27a:del]: ((p@(ap@(c_2Elist_2EALL__DISTINCT@A_27a)@(c_2Elist_2ENIL@A_27a))) <=> $true))).
thf(conj_thm_2EHolSmt_2EALL__DISTINCT__CONS,lemma,( ! [A_27a:del]: ( ! [V0h:$i] : ((mem@V0h@A_27a) => ( ! [V1t:$i] : ((mem@V1t@(ty_2Elist_2Elist@A_27a)) => ((p@(ap@(c_2Elist_2EALL__DISTINCT@A_27a)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V0h)@V1t))) <=> ((~~ (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0h)@(ap@(c_2Elist_2ELIST__TO__SET@A_27a)@V1t)))) & (p@(ap@(c_2Elist_2EALL__DISTINCT@A_27a)@V1t)))))))))).
thf(conj_thm_2EHolSmt_2ENOT__MEM__NIL,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((~~ (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(ap@(c_2Elist_2ELIST__TO__SET@A_27a)@(c_2Elist_2ENIL@A_27a))))) <=> $true))))).
thf(conj_thm_2EHolSmt_2ENOT__MEM__CONS,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1h:$i] : ((mem@V1h@A_27a) => ( ! [V2t:$i] : ((mem@V2t@(ty_2Elist_2Elist@A_27a)) => ((~~ (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(ap@(c_2Elist_2ELIST__TO__SET@A_27a)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V1h)@V2t))))) <=> ((~~ (V0x = V1h)) & (~~ (p@(ap@(ap@(c_2Ebool_2EIN@A_27a)@V0x)@(ap@(c_2Elist_2ELIST__TO__SET@A_27a)@V2t)))))))))))))).
thf(conj_thm_2EHolSmt_2EAND__T,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) & $true) <=> (p@V0p))))).
thf(conj_thm_2EHolSmt_2ET__AND,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((($true & (p@V0p)) <=> ($true & (p@V1q))) => ((p@V0p) <=> (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2EF__OR,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((($false | (p@V0p)) <=> ($false | (p@V1q))) => ((p@V0p) <=> (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2ECONJ__CONG,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ( ! [V3s:$i] : ((mem@V3s@bool) => (((p@V0p) <=> (p@V1q)) => (((p@V2r) <=> (p@V3s)) => (((p@V0p) & (p@V2r)) <=> ((p@V1q) & (p@V3s)))))))))))))).
thf(conj_thm_2EHolSmt_2ENOT__NOT__ELIM,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ((~~ (~~ (p@V0p))) => (p@V0p))))).
thf(conj_thm_2EHolSmt_2ENOT__FALSE,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ((p@V0p) => ((~~ (p@V0p)) => $false))))).
thf(conj_thm_2EHolSmt_2ENNF__CONJ,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ( ! [V3s:$i] : ((mem@V3s@bool) => (((~~ (p@V0p)) <=> (p@V2r)) => (((~~ (p@V1q)) <=> (p@V3s)) => ((~~ ((p@V0p) & (p@V1q))) <=> ((p@V2r) | (p@V3s)))))))))))))).
thf(conj_thm_2EHolSmt_2ENNF__DISJ,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ( ! [V3s:$i] : ((mem@V3s@bool) => (((~~ (p@V0p)) <=> (p@V2r)) => (((~~ (p@V1q)) <=> (p@V3s)) => ((~~ ((p@V0p) | (p@V1q))) <=> ((p@V2r) & (p@V3s)))))))))))))).
thf(conj_thm_2EHolSmt_2ENNF__NOT__NOT,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) <=> (p@V1q)) => ((~~ (~~ (p@V0p))) <=> (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2ENEG__IFF__1__1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V1q) <=> (p@V0p)) => (~~ ((p@V0p) <=> (~~ (p@V1q)))))))))).
thf(conj_thm_2EHolSmt_2ENEG__IFF__1__2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~~ ((p@V0p) <=> (~~ (p@V1q)))) => ((p@V1q) <=> (p@V0p)))))))).
thf(conj_thm_2EHolSmt_2ENEG__IFF__2__1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) <=> (~~ (p@V1q))) => (~~ ((p@V0p) <=> (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2ENEG__IFF__2__2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~~ ((p@V0p) <=> (p@V1q))) => ((p@V0p) <=> (~~ (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2EDISJ__ELIM__1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((((p@V0p) | (p@V1q)) => (p@V2r)) => ((p@V0p) => (p@V2r)))))))))).
thf(conj_thm_2EHolSmt_2EDISJ__ELIM__2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((((p@V0p) | (p@V1q)) => (p@V2r)) => ((p@V1q) => (p@V2r)))))))))).
thf(conj_thm_2EHolSmt_2EIMP__DISJ__1,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) => (p@V1q)) => ((~~ (p@V0p)) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2EIMP__DISJ__2,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) => (p@V1q)) => ((p@V0p) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2EIMP__FALSE,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((~~ (p@V0p)) => $false) => (p@V0p))))).
thf(conj_thm_2EHolSmt_2EAND__IMP__INTRO__SYM,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((((p@V0p) & (p@V1q)) => (p@V2r)) <=> ((p@V0p) => ((p@V1q) => (p@V2r))))))))))).
thf(conj_thm_2EHolSmt_2EVALID__IFF__TRUE,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ((p@V0p) => ((p@V0p) <=> $true))))).
thf(conj_thm_2EHolSmt_2Ed001,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~~ ((p@V0p) <=> (p@V1q))) | ((~~ (p@V0p)) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Ed002,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~~ ((p@V0p) <=> (p@V1q))) | ((p@V0p) | (~~ (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2Ed003,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) <=> (~~ (p@V1q))) | ((~~ (p@V0p)) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Ed004,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) <=> (p@V1q)) | ((p@V0p) | (~~ (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2Ed005,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) <=> (p@V1q)) | ((~~ (p@V0p)) | (~~ (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2Ed006,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) <=> (p@V1q)) | ((p@V0p) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Ed007,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~~ ((~~ (p@V0p)) <=> (p@V1q))) | ((p@V0p) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Ed008,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~~ ((p@V0p) <=> (~~ (p@V1q)))) | ((p@V0p) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Ed009,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~~ (p@V0p)) | ((p@V1q) | (~~ ((p@V0p) <=> (p@V1q)))))))))).
thf(conj_thm_2EHolSmt_2Ed010,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((p@V0p) | ((~~ (p@V1q)) | (~~ ((p@V0p) <=> (p@V1q)))))))))).
thf(conj_thm_2EHolSmt_2Ed011,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((p@V0p) | ((p@V1q) | (~~ ((~~ (p@V0p)) <=> (p@V1q)))))))))).
thf(conj_thm_2EHolSmt_2Ed012,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((p@V0p) | ((p@V1q) | (~~ ((p@V0p) <=> (~~ (p@V1q))))))))))).
thf(conj_thm_2EHolSmt_2Ed013,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) & (~~ (p@V1q))) | ((p@V0p) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Ed014,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) & (p@V1q)) | ((p@V0p) | (~~ (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2Ed015,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) & (~~ (p@V1q))) | ((~~ (p@V0p)) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Ed016,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) & (p@V1q)) | ((~~ (p@V0p)) | (~~ (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2Ed017,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ( ! [V2x:$i] : ((mem@V2x@A_27a) => ((p@V0p) | (V1y = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V2x)@V1y))))))))))).
thf(conj_thm_2EHolSmt_2Ed018,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2y:$i] : ((mem@V2y@A_27a) => ((~~ (p@V0p)) | (V1x = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V1x)@V2y))))))))))).
thf(conj_thm_2EHolSmt_2Ed019,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2y:$i] : ((mem@V2y@A_27a) => ((p@V0p) | ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V1x)@V2y) = V2y)))))))))).
thf(conj_thm_2EHolSmt_2Ed020,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2y:$i] : ((mem@V2y@A_27a) => ((~~ (p@V0p)) | ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V1x)@V2y) = V1x)))))))))).
thf(conj_thm_2EHolSmt_2Ed021,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((p@V0p) | ((p@V1q) | (~~ (p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V2r)@V1q)))))))))))).
thf(conj_thm_2EHolSmt_2Ed022,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((~~ (p@V0p)) | ((p@V1q) | (~~ (p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@V2r)))))))))))).
thf(conj_thm_2EHolSmt_2Ed023,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@V2r)) | ((~~ (p@V0p)) | (~~ (p@V1q))))))))))).
thf(conj_thm_2EHolSmt_2Ed024,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@V2r)) | ((p@V0p) | (~~ (p@V2r))))))))))).
thf(conj_thm_2EHolSmt_2Ed025,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@(ap@c_2Ebool_2E_7E@V1q))@V2r)) | ((~~ (p@V0p)) | (p@V1q)))))))))).
thf(conj_thm_2EHolSmt_2Ed026,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@(ap@c_2Ebool_2E_7E@V2r))) | ((p@V0p) | (p@V2r)))))))))).
thf(conj_thm_2EHolSmt_2Ed027,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((~~ (p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@V2r))) | ((~~ (p@V0p)) | (p@V1q)))))))))).
thf(conj_thm_2EHolSmt_2Ed028,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((~~ (p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@V2r))) | ((p@V0p) | (p@V2r)))))))))).
thf(conj_thm_2EHolSmt_2Er001,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((V0x = V1y) <=> (V1y = V0x)))))))).
thf(conj_thm_2EHolSmt_2Er002,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((V0x = V0x) <=> $true))))).
thf(conj_thm_2EHolSmt_2Er003,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) <=> $true) <=> (p@V0p))))).
thf(conj_thm_2EHolSmt_2Er004,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (($true <=> (p@V0p)) <=> (p@V0p))))).
thf(conj_thm_2EHolSmt_2Er005,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) <=> $false) <=> (~~ (p@V0p)))))).
thf(conj_thm_2EHolSmt_2Er006,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (($false <=> (p@V0p)) <=> (~~ (p@V0p)))))).
thf(conj_thm_2EHolSmt_2Er007,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) <=> (~~ (p@V1q))) <=> ((p@V0p) <=> (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Er008,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~~ ((p@V0p) <=> (~~ (p@V1q)))) <=> ((p@V0p) <=> (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Er009,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((~~ ((~~ (p@V0p)) <=> (p@V1q))) <=> ((p@V0p) <=> (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Er010,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2ET)@V0x)@V1y) = V0x))))))).
thf(conj_thm_2EHolSmt_2Er011,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@c_2Ebool_2EF)@V0x)@V1y) = V1y))))))).
thf(conj_thm_2EHolSmt_2Er012,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@c_2Ebool_2ET)) <=> ((~~ (p@V0p)) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Er013,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@c_2Ebool_2ET)) <=> ((p@V1q) | (~~ (p@V0p))))))))).
thf(conj_thm_2EHolSmt_2Er014,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@(ap@c_2Ebool_2E_7E@V1q))) <=> ((p@V0p) <=> (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Er015,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@V1q)@(ap@c_2Ebool_2E_7E@V1q))) <=> ((p@V1q) <=> (p@V0p)))))))).
thf(conj_thm_2EHolSmt_2Er016,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@(ap@c_2Ebool_2E_7E@V1q))@V1q)) <=> ((p@V0p) <=> (~~ (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2Er017,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@(ap@c_2Ebool_2E_7E@V1q))@V1q)) <=> ((~~ (p@V1q)) <=> (p@V0p)))))))).
thf(conj_thm_2EHolSmt_2Er018,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2y:$i] : ((mem@V2y@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@(ap@c_2Ebool_2E_7E@V0p))@V1x)@V2y) = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V2y)@V1x)))))))))).
thf(conj_thm_2EHolSmt_2Er019,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2x:$i] : ((mem@V2x@A_27a) => ( ! [V3y:$i] : ((mem@V3y@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@(ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V1q)@V2x)@V3y))@V2x) = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@(ap@(ap@c_2Ebool_2E_2F_5C@V0p)@(ap@c_2Ebool_2E_7E@V1q)))@V3y)@V2x)))))))))))).
thf(conj_thm_2EHolSmt_2Er020,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2x:$i] : ((mem@V2x@A_27a) => ( ! [V3y:$i] : ((mem@V3y@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@(ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V1q)@V2x)@V3y))@V2x) = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@(ap@(ap@c_2Ebool_2E_2F_5C@(ap@c_2Ebool_2E_7E@V1q))@V0p))@V3y)@V2x)))))))))))).
thf(conj_thm_2EHolSmt_2Er021,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2x:$i] : ((mem@V2x@A_27a) => ( ! [V3y:$i] : ((mem@V3y@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@(ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V1q)@V2x)@V3y))@V3y) = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@(ap@(ap@c_2Ebool_2E_2F_5C@V0p)@V1q))@V2x)@V3y)))))))))))).
thf(conj_thm_2EHolSmt_2Er022,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2x:$i] : ((mem@V2x@A_27a) => ( ! [V3y:$i] : ((mem@V3y@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@(ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V1q)@V2x)@V3y))@V3y) = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@(ap@(ap@c_2Ebool_2E_2F_5C@V1q)@V0p))@V2x)@V3y)))))))))))).
thf(conj_thm_2EHolSmt_2Er023,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2y:$i] : ((mem@V2y@A_27a) => ( ! [V3z:$i] : ((mem@V3z@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V1x)@(ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V2y)@V3z)) = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V1x)@V3z)))))))))))).
thf(conj_thm_2EHolSmt_2Er024,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2q:$i] : ((mem@V2q@bool) => ( ! [V3y:$i] : ((mem@V3y@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V1x)@(ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V2q)@V1x)@V3y)) = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@(ap@(ap@c_2Ebool_2E_5C_2F@V0p)@V2q))@V1x)@V3y)))))))))))).
thf(conj_thm_2EHolSmt_2Er025,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2q:$i] : ((mem@V2q@bool) => ( ! [V3y:$i] : ((mem@V3y@A_27a) => ((ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V1x)@(ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V2q)@V1x)@V3y)) = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@(ap@(ap@c_2Ebool_2E_5C_2F@V2q)@V0p))@V1x)@V3y)))))))))))).
thf(conj_thm_2EHolSmt_2Er026,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2y:$i] : ((mem@V2y@A_27a) => ( ! [V3z:$i] : ((mem@V3z@A_27a) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@(ap@(ap@(c_2Emin_2E_3D@A_27a)@V1x)@V2y))@(ap@(ap@(c_2Emin_2E_3D@A_27a)@V1x)@V3z))) <=> (V1x = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V2y)@V3z))))))))))))).
thf(conj_thm_2EHolSmt_2Er027,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2y:$i] : ((mem@V2y@A_27a) => ( ! [V3z:$i] : ((mem@V3z@A_27a) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@(ap@(ap@(c_2Emin_2E_3D@A_27a)@V1x)@V2y))@(ap@(ap@(c_2Emin_2E_3D@A_27a)@V2y)@V3z))) <=> (V2y = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V1x)@V3z))))))))))))).
thf(conj_thm_2EHolSmt_2Er028,lemma,( ! [A_27a:del]: ( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:$i] : ((mem@V1x@A_27a) => ( ! [V2y:$i] : ((mem@V2y@A_27a) => ( ! [V3z:$i] : ((mem@V3z@A_27a) => ((p@(ap@(ap@(ap@(c_2Ebool_2ECOND@bool)@V0p)@(ap@(ap@(c_2Emin_2E_3D@A_27a)@V1x)@V2y))@(ap@(ap@(c_2Emin_2E_3D@A_27a)@V3z)@V2y))) <=> (V2y = (ap@(ap@(ap@(c_2Ebool_2ECOND@A_27a)@V0p)@V1x)@V3z))))))))))))).
thf(conj_thm_2EHolSmt_2Er029,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) => (p@V1q)) <=> ((p@V0p) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Er030,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) => (p@V1q)) <=> ((p@V1q) | (p@V0p)))))))).
thf(conj_thm_2EHolSmt_2Er031,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) => (p@V1q)) <=> ((~~ (p@V0p)) | (p@V1q)))))))).
thf(conj_thm_2EHolSmt_2Er032,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) => (p@V1q)) <=> ((p@V1q) | (~~ (p@V0p))))))))).
thf(conj_thm_2EHolSmt_2Er033,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (($true => (p@V0p)) <=> (p@V0p))))).
thf(conj_thm_2EHolSmt_2Er034,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) => $true) <=> $true)))).
thf(conj_thm_2EHolSmt_2Er035,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (($false => (p@V0p)) <=> $true)))).
thf(conj_thm_2EHolSmt_2Er036,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) => (p@V0p)) <=> $true)))).
thf(conj_thm_2EHolSmt_2Er037,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => ( ! [V2r:$i] : ((mem@V2r@bool) => ((((p@V0p) <=> (p@V1q)) => (p@V2r)) <=> ((p@V2r) | ((p@V1q) <=> (~~ (p@V0p)))))))))))).
thf(conj_thm_2EHolSmt_2Er038,lemma,((~~ ($true)) <=> $false)).
thf(conj_thm_2EHolSmt_2Er039,lemma,((~~ ($false)) <=> $true)).
thf(conj_thm_2EHolSmt_2Er040,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ((~~ (~~ (p@V0p))) <=> (p@V0p))))).
thf(conj_thm_2EHolSmt_2Er041,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) | (p@V1q)) <=> ((p@V1q) | (p@V0p)))))))).
thf(conj_thm_2EHolSmt_2Er042,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) | $true) <=> $true)))).
thf(conj_thm_2EHolSmt_2Er043,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) | (~~ (p@V0p))) <=> $true)))).
thf(conj_thm_2EHolSmt_2Er044,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((~~ (p@V0p)) | (p@V0p)) <=> $true)))).
thf(conj_thm_2EHolSmt_2Er045,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (($true | (p@V0p)) <=> $true)))).
thf(conj_thm_2EHolSmt_2Er046,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) | $false) <=> (p@V0p))))).
thf(conj_thm_2EHolSmt_2Er047,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (($false | (p@V0p)) <=> (p@V0p))))).
thf(conj_thm_2EHolSmt_2Er048,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) & (p@V1q)) <=> ((p@V1q) & (p@V0p)))))))).
thf(conj_thm_2EHolSmt_2Er049,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) & $true) <=> (p@V0p))))).
thf(conj_thm_2EHolSmt_2Er050,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (($true & (p@V0p)) <=> (p@V0p))))).
thf(conj_thm_2EHolSmt_2Er051,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (((p@V0p) & $false) <=> $false)))).
thf(conj_thm_2EHolSmt_2Er052,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => (($false & (p@V0p)) <=> $false)))).
thf(conj_thm_2EHolSmt_2Er053,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) & (p@V1q)) <=> (~~ ((~~ (p@V0p)) | (~~ (p@V1q)))))))))).
thf(conj_thm_2EHolSmt_2Er054,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) & (p@V1q)) <=> (~~ ((p@V0p) | (~~ (p@V1q)))))))))).
thf(conj_thm_2EHolSmt_2Er055,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) & (~~ (p@V1q))) <=> (~~ ((~~ (p@V0p)) | (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2Er056,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) & (~~ (p@V1q))) <=> (~~ ((p@V0p) | (p@V1q))))))))).
thf(conj_thm_2EHolSmt_2Er057,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) & (p@V1q)) <=> (~~ ((~~ (p@V1q)) | (~~ (p@V0p)))))))))).
thf(conj_thm_2EHolSmt_2Er058,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) & (p@V1q)) <=> (~~ ((~~ (p@V1q)) | (p@V0p))))))))).
thf(conj_thm_2EHolSmt_2Er059,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((p@V0p) & (~~ (p@V1q))) <=> (~~ ((p@V1q) | (~~ (p@V0p)))))))))).
thf(conj_thm_2EHolSmt_2Er060,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1q:$i] : ((mem@V1q@bool) => (((~~ (p@V0p)) & (~~ (p@V1q))) <=> (~~ ((p@V1q) | (p@V0p))))))))).
thf(conj_thm_2EHolSmt_2Er061,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1f:$i] : ((mem@V1f@(arr@A_27a@A_27b)) => ((ap@(ap@(ap@(c_2Ecombin_2EUPDATE@A_27a@A_27b)@V0x)@(ap@V1f@V0x))@V1f) = V1f)))))))).
thf(conj_thm_2EHolSmt_2Er062,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ((p@(ap@(c_2Elist_2EALL__DISTINCT@A_27a)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V0x)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V0x)@(c_2Elist_2ENIL@A_27a))))) <=> $false))))).
thf(conj_thm_2EHolSmt_2Er063,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((p@(ap@(c_2Elist_2EALL__DISTINCT@A_27a)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V0x)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V1y)@(c_2Elist_2ENIL@A_27a))))) <=> (~~ (V0x = V1y))))))))).
thf(conj_thm_2EHolSmt_2Er064,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ((p@(ap@(c_2Elist_2EALL__DISTINCT@A_27a)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V0x)@(ap@(ap@(c_2Elist_2ECONS@A_27a)@V1y)@(c_2Elist_2ENIL@A_27a))))) <=> (~~ (V1y = V0x))))))))).
thf(conj_thm_2EHolSmt_2Er065,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((V0x = V1y) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er066,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((V0x = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z)))) = V1y)))))).
thf(conj_thm_2EHolSmt_2Er067,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((V0x = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z))))) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z)))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er068,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((V0x = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z)))@(inj__ty_2Einteger_2Eint @ V0x)))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er069,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((V0x = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z))))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er070,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((V0x = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er071,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((V0x = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))@(inj__ty_2Einteger_2Eint @ V2z)))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er072,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((V0x = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y))))))))).
thf(conj_thm_2EHolSmt_2Er073,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((V0x = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))) = V1y)))))).
thf(conj_thm_2EHolSmt_2Er074,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : (((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y)))) <=> (V0x = V1y))))).
thf(conj_thm_2EHolSmt_2Er075,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : (((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))@(inj__ty_2Einteger_2Eint @ V1y))) = V2z) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V2z))))))))).
thf(conj_thm_2EHolSmt_2Er076,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : (((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (V1y = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V0x)))))))).
thf(conj_thm_2EHolSmt_2Er077,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : (((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) = V2z) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z)))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V0x))))))))).
thf(conj_thm_2EHolSmt_2Er078,lemma,( ! [V0a:tp__ty_2Einteger_2Eint] : ( ! [V1x:tp__ty_2Einteger_2Eint] : ( ! [V2v:tp__ty_2Einteger_2Eint] : ( ! [V3y:tp__ty_2Einteger_2Eint] : ( ! [V4w:tp__ty_2Einteger_2Eint] : ( ! [V5z:tp__ty_2Einteger_2Eint] : (((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0a))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1x)))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(inj__ty_2Einteger_2Eint @ V2v))@(inj__ty_2Einteger_2Eint @ V3y)))@(ap@(ap@c_2Einteger_2Eint__mul@(inj__ty_2Einteger_2Eint @ V4w))@(inj__ty_2Einteger_2Eint @ V5z)))))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V2v)))@(inj__ty_2Einteger_2Eint @ V3y)))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V4w)))@(inj__ty_2Einteger_2Eint @ V5z))))) = V0a))))))))).
thf(conj_thm_2EHolSmt_2Er079,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Einteger_2Eint @ V0x))) = V0x))).
thf(conj_thm_2EHolSmt_2Er080,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = V0x))).
thf(conj_thm_2EHolSmt_2Er081,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V0x))))))).
thf(conj_thm_2EHolSmt_2Er082,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V0x))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Einteger_2Eint @ V0x)))))).
thf(conj_thm_2EHolSmt_2Er083,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z))))))))).
thf(conj_thm_2EHolSmt_2Er084,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(inj__ty_2Einteger_2Eint @ V1y))))))))).
thf(conj_thm_2EHolSmt_2Er085,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(inj__ty_2Einteger_2Eint @ V0x))))))))).
thf(conj_thm_2EHolSmt_2Er086,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V2z))))))))).
thf(conj_thm_2EHolSmt_2Er087,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ( ! [V3u:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(inj__ty_2Einteger_2Eint @ V3u))))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V3u))@(inj__ty_2Einteger_2Eint @ V0x))))))))))).
thf(conj_thm_2EHolSmt_2Er088,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V0x))) <=> $true))).
thf(conj_thm_2EHolSmt_2Er089,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er090,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er091,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er092,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2EHolSmt_2Er093,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))))))).
thf(conj_thm_2EHolSmt_2Er094,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))@(inj__ty_2Einteger_2Eint @ V1y)))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er095,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V0x))))))).
thf(conj_thm_2EHolSmt_2Er096,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__gt@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V0x)))))))).
thf(conj_thm_2EHolSmt_2Er097,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__gt@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y)))))))).
thf(conj_thm_2EHolSmt_2Er098,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__gt@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er099,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__gt@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er100,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__gt@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))))@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y)))))))))).
thf(conj_thm_2EHolSmt_2Er101,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V0x))) <=> $true))).
thf(conj_thm_2EHolSmt_2Er102,lemma,((p@(ap@(ap@c_2Einteger_2Eint__le@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> $true)).
thf(conj_thm_2EHolSmt_2Er103,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V0x))))))).
thf(conj_thm_2EHolSmt_2Er104,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V0x)))@(inj__ty_2Einteger_2Eint @ V1y)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V0x))))))).
thf(conj_thm_2EHolSmt_2Er105,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2EHolSmt_2Er106,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er107,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er108,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))@(inj__ty_2Einteger_2Eint @ V1y)))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er109,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))@(inj__ty_2Einteger_2Eint @ V1y)))@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V2z)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(inj__ty_2Einteger_2Eint @ V2z)))))))).
thf(conj_thm_2EHolSmt_2Er110,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V0x)))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z))))@(inj__ty_2Einteger_2Eint @ V0x)))))))).
thf(conj_thm_2EHolSmt_2Er111,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(inj__ty_2Einteger_2Eint @ V2z))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z)))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er112,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z))))@(inj__ty_2Einteger_2Eint @ V1y)))))))).
thf(conj_thm_2EHolSmt_2Er113,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))))@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y))))))))).
thf(conj_thm_2EHolSmt_2Er114,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z)))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er115,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V0x)))))))).
thf(conj_thm_2EHolSmt_2Er116,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y)))))))).
thf(conj_thm_2EHolSmt_2Er117,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er118,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er119,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z))))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(inj__ty_2Einteger_2Eint @ V2z)))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2EHolSmt_2Er120,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z))))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2EHolSmt_2Er121,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z)))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))))@(inj__ty_2Einteger_2Eint @ V1y))))))))).
thf(conj_thm_2EHolSmt_2Er122,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ( ! [V3u:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y)))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(inj__ty_2Einteger_2Eint @ V3u))))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V3u))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))))@(inj__ty_2Einteger_2Eint @ V1y)))))))))).
thf(conj_thm_2EHolSmt_2Er123,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ( ! [V3u:tp__ty_2Einteger_2Eint] : ( ! [V4v:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y)))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V3u))@(inj__ty_2Einteger_2Eint @ V4v)))))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V3u))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V4v))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x))))))@(inj__ty_2Einteger_2Eint @ V1y))))))))))).
thf(conj_thm_2EHolSmt_2Er124,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V0x)))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z))))@(inj__ty_2Einteger_2Eint @ V0x))))))))).
thf(conj_thm_2EHolSmt_2Er125,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V2z))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(inj__ty_2Einteger_2Eint @ V0x))))))))).
thf(conj_thm_2EHolSmt_2Er126,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__lt@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V0x)))@(inj__ty_2Einteger_2Eint @ V1y)))) <=> (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V1y))@(inj__ty_2Einteger_2Eint @ V0x)))))))).
thf(conj_thm_2EHolSmt_2Er127,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__sub@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = V0x))).
thf(conj_thm_2EHolSmt_2Er128,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__sub@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Einteger_2Eint @ V0x))) = (surj__ty_2Einteger_2Eint @ (ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V0x)))))).
thf(conj_thm_2EHolSmt_2Er129,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__sub@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Einteger_2Eint @ V0x))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))))).
thf(conj_thm_2EHolSmt_2Er130,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__sub@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V0x))))))).
thf(conj_thm_2EHolSmt_2Er131,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__sub@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))))))).
thf(conj_thm_2EHolSmt_2Er132,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__sub@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V0x))))))).
thf(conj_thm_2EHolSmt_2Er133,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__sub@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V0x)))))).
thf(conj_thm_2EHolSmt_2Er134,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__sub@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V1y))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z)))))))))).
thf(conj_thm_2EHolSmt_2Er135,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ( ! [V2z:tp__ty_2Einteger_2Eint] : ((surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__sub@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y)))@(inj__ty_2Einteger_2Eint @ V2z))) = (surj__ty_2Einteger_2Eint @ (ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__add@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V2z)))@(inj__ty_2Einteger_2Eint @ V1y))))))))).
thf(conj_thm_2EHolSmt_2Er136,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er137,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))))))))).
thf(conj_thm_2EHolSmt_2Er138,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V3z))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2y))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0a)))@(inj__ty_2Erealax_2Ereal @ V3z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2EHolSmt_2Er139,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2y))@(inj__ty_2Erealax_2Ereal @ V3z))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2y))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V3z))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0a)))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2EHolSmt_2Er140,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4z))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4z)))@(inj__ty_2Erealax_2Ereal @ V0a)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))).
thf(conj_thm_2EHolSmt_2Er141,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4z))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0a))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))).
thf(conj_thm_2EHolSmt_2Er142,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))) = V0a)))))))).
thf(conj_thm_2EHolSmt_2Er143,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : ( ! [V5w:tp__ty_2Erealax_2Ereal] : ( ! [V6z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V5w))@(inj__ty_2Erealax_2Ereal @ V6z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5w)))@(inj__ty_2Erealax_2Ereal @ V6z)))@(inj__ty_2Erealax_2Ereal @ V0a))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))))).
thf(conj_thm_2EHolSmt_2Er144,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : ( ! [V5w:tp__ty_2Erealax_2Ereal] : ( ! [V6z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V5w))@(inj__ty_2Erealax_2Ereal @ V6z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5w)))@(inj__ty_2Erealax_2Ereal @ V6z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))))))))))))).
thf(conj_thm_2EHolSmt_2Er145,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : ( ! [V5w:tp__ty_2Erealax_2Ereal] : ( ! [V6z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5w)))@(inj__ty_2Erealax_2Ereal @ V6z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V5w))@(inj__ty_2Erealax_2Ereal @ V6z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))))))))))))).
thf(conj_thm_2EHolSmt_2Er146,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : ( ! [V5w:tp__ty_2Erealax_2Ereal] : ( ! [V6z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V5w))@(inj__ty_2Erealax_2Ereal @ V6z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5w)))@(inj__ty_2Erealax_2Ereal @ V6z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))))))))))))).
thf(conj_thm_2EHolSmt_2Er147,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : ( ! [V5w:tp__ty_2Erealax_2Ereal] : ( ! [V6z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5w)))@(inj__ty_2Erealax_2Ereal @ V6z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V5w))@(inj__ty_2Erealax_2Ereal @ V6z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))))))))))))).
thf(conj_thm_2EHolSmt_2Er148,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : ( ! [V5w:tp__ty_2Erealax_2Ereal] : ( ! [V6z:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V5w))@(inj__ty_2Erealax_2Ereal @ V6z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5w)))@(inj__ty_2Erealax_2Ereal @ V6z))))) = V0a)))))))))).
thf(conj_thm_2EHolSmt_2Er149,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : ( ! [V5w:tp__ty_2Erealax_2Ereal] : ( ! [V6z:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5w)))@(inj__ty_2Erealax_2Ereal @ V6z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V5w))@(inj__ty_2Erealax_2Ereal @ V6z))))) = V0a)))))))))).
thf(conj_thm_2EHolSmt_2Er150,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : ( ! [V5w:tp__ty_2Erealax_2Ereal] : ( ! [V6z:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V5w))@(inj__ty_2Erealax_2Ereal @ V6z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5w)))@(inj__ty_2Erealax_2Ereal @ V6z))))) = V0a)))))))))).
thf(conj_thm_2EHolSmt_2Er151,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3v:tp__ty_2Erealax_2Ereal] : ( ! [V4y:tp__ty_2Erealax_2Ereal] : ( ! [V5w:tp__ty_2Erealax_2Ereal] : ( ! [V6z:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3v)))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5w)))@(inj__ty_2Erealax_2Ereal @ V6z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3v))@(inj__ty_2Erealax_2Ereal @ V4y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V5w))@(inj__ty_2Erealax_2Ereal @ V6z))))) = V0a)))))))))).
thf(conj_thm_2EHolSmt_2Er152,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V3y))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a)))))))))))).
thf(conj_thm_2EHolSmt_2Er153,lemma,( ! [V0a:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2x:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ((V0a = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2x)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V3y))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0a)))))))))))).
thf(conj_thm_2EHolSmt_2Er154,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4a:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4a)))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))) = V4a)))))))).
thf(conj_thm_2EHolSmt_2Er155,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a)))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z))))) = V5a))))))))).
thf(conj_thm_2EHolSmt_2Er156,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z))))) = V6a)))))))))).
thf(conj_thm_2EHolSmt_2Er157,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z))))) = V6a)))))))))).
thf(conj_thm_2EHolSmt_2Er158,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : (((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z))))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z))))) = V6a)))))))))).
thf(conj_thm_2EHolSmt_2Er159,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2EHolSmt_2Er160,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__ge@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er161,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__gt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Er162,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Er163,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V2z))))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2EHolSmt_2Er164,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(inj__ty_2Erealax_2Ereal @ V2a))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2a))))))))).
thf(conj_thm_2EHolSmt_2Er165,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2a)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(inj__ty_2Erealax_2Ereal @ V2a)))))))).
thf(conj_thm_2EHolSmt_2Er166,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2EHolSmt_2Er167,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(inj__ty_2Erealax_2Ereal @ V4a))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4a))))))))))).
thf(conj_thm_2EHolSmt_2Er168,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4a)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(inj__ty_2Erealax_2Ereal @ V4a)))))))))).
thf(conj_thm_2EHolSmt_2Er169,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(inj__ty_2Erealax_2Ereal @ V4a))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4a))))))))))).
thf(conj_thm_2EHolSmt_2Er170,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4a)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(inj__ty_2Erealax_2Ereal @ V4a)))))))))).
thf(conj_thm_2EHolSmt_2Er171,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))))).
thf(conj_thm_2EHolSmt_2Er172,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))))).
thf(conj_thm_2EHolSmt_2Er173,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))))).
thf(conj_thm_2EHolSmt_2Er174,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))))).
thf(conj_thm_2EHolSmt_2Er175,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a))))))))))))).
thf(conj_thm_2EHolSmt_2Er176,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a)))))))))))).
thf(conj_thm_2EHolSmt_2Er177,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a))))))))))))).
thf(conj_thm_2EHolSmt_2Er178,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a)))))))))))).
thf(conj_thm_2EHolSmt_2Er179,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a))))))))))))).
thf(conj_thm_2EHolSmt_2Er180,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a)))))))))))).
thf(conj_thm_2EHolSmt_2Er181,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a))))))))))))).
thf(conj_thm_2EHolSmt_2Er182,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a)))))))))))).
thf(conj_thm_2EHolSmt_2Er183,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a)))) <=> (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a))))))))))).
thf(conj_thm_2EHolSmt_2Er184,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__ge@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2EHolSmt_2Er185,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(inj__ty_2Erealax_2Ereal @ V2a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2a)))))))))).
thf(conj_thm_2EHolSmt_2Er186,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(inj__ty_2Erealax_2Ereal @ V2a))))))))).
thf(conj_thm_2EHolSmt_2Er187,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))).
thf(conj_thm_2EHolSmt_2Er188,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))).
thf(conj_thm_2EHolSmt_2Er189,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(inj__ty_2Erealax_2Ereal @ V4a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4a)))))))))))).
thf(conj_thm_2EHolSmt_2Er190,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(inj__ty_2Erealax_2Ereal @ V4a))))))))))).
thf(conj_thm_2EHolSmt_2Er191,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(inj__ty_2Erealax_2Ereal @ V4a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4a)))))))))))).
thf(conj_thm_2EHolSmt_2Er192,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y))))@(inj__ty_2Erealax_2Ereal @ V4a))))))))))).
thf(conj_thm_2EHolSmt_2Er193,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))))))))))))).
thf(conj_thm_2EHolSmt_2Er194,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))))))))))))).
thf(conj_thm_2EHolSmt_2Er195,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))))))))))))).
thf(conj_thm_2EHolSmt_2Er196,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))))))))))))).
thf(conj_thm_2EHolSmt_2Er197,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))))))))))))).
thf(conj_thm_2EHolSmt_2Er198,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))))))))))))).
thf(conj_thm_2EHolSmt_2Er199,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))))))))))))).
thf(conj_thm_2EHolSmt_2Er200,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ( ! [V6a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V6a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(inj__ty_2Erealax_2Ereal @ V6a))))))))))))).
thf(conj_thm_2EHolSmt_2Er201,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))))).
thf(conj_thm_2EHolSmt_2Er202,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4w:tp__ty_2Erealax_2Ereal] : ( ! [V5z:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V4w)))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V4w))@(inj__ty_2Erealax_2Ereal @ V5z)))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))))))).
thf(conj_thm_2EHolSmt_2Er203,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a))))))))))))).
thf(conj_thm_2EHolSmt_2Er204,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a)))))))))))).
thf(conj_thm_2EHolSmt_2Er205,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a))))))))))))).
thf(conj_thm_2EHolSmt_2Er206,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a)))))))))))).
thf(conj_thm_2EHolSmt_2Er207,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a))))))))))))).
thf(conj_thm_2EHolSmt_2Er208,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a)))))))))))).
thf(conj_thm_2EHolSmt_2Er209,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a))))))))))))).
thf(conj_thm_2EHolSmt_2Er210,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1v:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V0x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1v)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1v))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a)))))))))))).
thf(conj_thm_2EHolSmt_2Er211,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ( ! [V3w:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V2y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V3w)))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2y))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V3w))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(inj__ty_2Erealax_2Ereal @ V5a)))))))))))).
thf(conj_thm_2EHolSmt_2Er212,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ( ! [V2v:tp__ty_2Erealax_2Ereal] : ( ! [V3y:tp__ty_2Erealax_2Ereal] : ( ! [V4z:tp__ty_2Erealax_2Ereal] : ( ! [V5a:tp__ty_2Erealax_2Ereal] : ((p@(ap@(ap@c_2Erealax_2Ereal__lt@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2v))@(inj__ty_2Erealax_2Ereal @ V3y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V4z)))))@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V5a)))) <=> (~~ (p@(ap@(ap@c_2Ereal_2Ereal__lte@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2v)))@(inj__ty_2Erealax_2Ereal @ V3y)))@(inj__ty_2Erealax_2Ereal @ V4z))))@(inj__ty_2Erealax_2Ereal @ V5a)))))))))))).
thf(conj_thm_2EHolSmt_2Er213,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) = V0x))).
thf(conj_thm_2EHolSmt_2Er214,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = V0x))).
thf(conj_thm_2EHolSmt_2Er215,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2EHolSmt_2Er216,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2EHolSmt_2Er217,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2EHolSmt_2Er218,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2EHolSmt_2Er219,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V2z))@(inj__ty_2Erealax_2Ereal @ V0x))))))))).
thf(conj_thm_2EHolSmt_2Er220,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(inj__ty_2Erealax_2Ereal @ V2z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V2z))))))))).
thf(conj_thm_2EHolSmt_2Er221,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0x)))))).
thf(conj_thm_2EHolSmt_2Er222,lemma,( ! [V0u:tp__ty_2Erealax_2Ereal] : ( ! [V1x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V0u))@(inj__ty_2Erealax_2Ereal @ V1x)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V0u)))@(inj__ty_2Erealax_2Ereal @ V1x))))))).
thf(conj_thm_2EHolSmt_2Er223,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) = V0x))).
thf(conj_thm_2EHolSmt_2Er224,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V1y)))))))).
thf(conj_thm_2EHolSmt_2Er225,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V0x))))))).
thf(conj_thm_2EHolSmt_2Er226,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2y))))))))).
thf(conj_thm_2EHolSmt_2Er227,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1u:tp__ty_2Erealax_2Ereal] : ( ! [V2y:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V1u))@(inj__ty_2Erealax_2Ereal @ V2y)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V1u)))@(inj__ty_2Erealax_2Ereal @ V2y)))@(inj__ty_2Erealax_2Ereal @ V0x)))))))).
thf(conj_thm_2EHolSmt_2Er228,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V2z)))))))))).
thf(conj_thm_2EHolSmt_2Er229,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(inj__ty_2Erealax_2Ereal @ V2z))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V2z)))@(inj__ty_2Erealax_2Ereal @ V1y))))))))).
thf(conj_thm_2EHolSmt_2Er230,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2u:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2u))@(inj__ty_2Erealax_2Ereal @ V3z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2u)))@(inj__ty_2Erealax_2Ereal @ V3z)))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))))))))).
thf(conj_thm_2EHolSmt_2Er231,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2u:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2u))@(inj__ty_2Erealax_2Ereal @ V3z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2u)))@(inj__ty_2Erealax_2Ereal @ V3z)))@(inj__ty_2Erealax_2Ereal @ V1y)))))))))).
thf(conj_thm_2EHolSmt_2Er232,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ( ! [V2u:tp__ty_2Erealax_2Ereal] : ( ! [V3z:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Ereal_2Ereal__sub@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(inj__ty_2Erealax_2Ereal @ V1y)))@(ap@(ap@c_2Erealax_2Ereal__mul@(inj__ty_2Erealax_2Ereal @ V2u))@(inj__ty_2Erealax_2Ereal @ V3z)))) = (surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V1y))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(inj__ty_2Erealax_2Ereal @ V2u)))@(inj__ty_2Erealax_2Ereal @ V3z))))))))))).
thf(conj_thm_2EHolSmt_2Er233,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(inj__ty_2Erealax_2Ereal @ V0x))) = (surj__ty_2Erealax_2Ereal @ (ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2EHolSmt_2Er234,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ((surj__ty_2Erealax_2Ereal @ (ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(inj__ty_2Erealax_2Ereal @ V0x))) = V0x))).
thf(conj_thm_2EHolSmt_2Er235,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__add@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V0x) = V0x))))).
thf(conj_thm_2EHolSmt_2Er236,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__add@A_27a)@V0x)@V1y) = (ap@(ap@(c_2Ewords_2Eword__add@A_27a)@V1y)@V0x)))))))).
thf(conj_thm_2EHolSmt_2Er237,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__add@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(ap@(c_2Ewords_2Eword__add@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@V0x)) = (ap@(ap@(c_2Ewords_2Eword__add@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@V0x)))))).
thf(conj_thm_2EHolSmt_2Er238,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1z:$i] : ((mem@V1z@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V2y:$i] : ((mem@V2y@(ty_2Efcp_2Ecart@bool@A_27a)) => (((ap@(ap@(c_2Ewords_2Eword__add@A_27a)@V0x)@V1z) = (ap@(ap@(c_2Ewords_2Eword__add@A_27a)@V2y)@V0x)) <=> (V2y = V1z)))))))))).
thf(conj_thm_2EHolSmt_2Er239,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0x:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0x))@(ap@(c_2Ewords_2Edimword@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))) => ((p@(ap@(c_2Epred__set_2EFINITE@A_27a)@(c_2Epred__set_2EUNIV@A_27a))) => ((ap@(ap@(c_2Ewords_2Eword__concat@A_27a@A_27b@A_27c)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@(ap@(c_2Ewords_2En2w@A_27b)@(inj__ty_2Enum_2Enum @ V0x))) = (ap@(c_2Ewords_2En2w@A_27c)@(inj__ty_2Enum_2Enum @ V0x)))))))))).
thf(conj_thm_2EHolSmt_2Er240,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:tp__ty_2Enum_2Enum] : ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0x))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))) => ((ap@(c_2Ewords_2Ew2w@A_27a@A_27b)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ V0x))) = (ap@(c_2Ewords_2En2w@A_27b)@(inj__ty_2Enum_2Enum @ V0x)))))))).
thf(conj_thm_2EHolSmt_2Er241,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0y:tp__ty_2Enum_2Enum] : ( ! [V1x:$i] : ((mem@V1x@(ty_2Efcp_2Ecart@bool@A_27b)) => ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(c_2Efcp_2Edimindex@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))@(ap@(c_2Efcp_2Edimindex@A_27c)@(c_2Ebool_2Ethe__value@A_27c)))) => ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0y))@(ap@(c_2Ewords_2Edimword@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))) => ((p@(ap@(c_2Epred__set_2EFINITE@A_27a)@(c_2Epred__set_2EUNIV@A_27a))) => (((ap@(ap@(c_2Ewords_2Eword__concat@A_27a@A_27b@A_27c)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V1x) = (ap@(c_2Ewords_2En2w@A_27c)@(inj__ty_2Enum_2Enum @ V0y))) <=> (V1x = (ap@(c_2Ewords_2En2w@A_27b)@(inj__ty_2Enum_2Enum @ V0y)))))))))))))).
thf(conj_thm_2EHolSmt_2Er242,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0y:tp__ty_2Enum_2Enum] : ( ! [V1x:$i] : ((mem@V1x@(ty_2Efcp_2Ecart@bool@A_27b)) => ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(c_2Efcp_2Edimindex@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))@(ap@(c_2Efcp_2Edimindex@A_27c)@(c_2Ebool_2Ethe__value@A_27c)))) => ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0y))@(ap@(c_2Ewords_2Edimword@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))) => ((p@(ap@(c_2Epred__set_2EFINITE@A_27a)@(c_2Epred__set_2EUNIV@A_27a))) => (((ap@(ap@(c_2Ewords_2Eword__concat@A_27a@A_27b@A_27c)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V1x) = (ap@(c_2Ewords_2En2w@A_27c)@(inj__ty_2Enum_2Enum @ V0y))) <=> ((ap@(c_2Ewords_2En2w@A_27b)@(inj__ty_2Enum_2Enum @ V0y)) = V1x)))))))))))).
thf(conj_thm_2EHolSmt_2Er243,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0y:tp__ty_2Enum_2Enum] : ( ! [V1x:$i] : ((mem@V1x@(ty_2Efcp_2Ecart@bool@A_27b)) => ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(c_2Efcp_2Edimindex@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))@(ap@(c_2Efcp_2Edimindex@A_27c)@(c_2Ebool_2Ethe__value@A_27c)))) => ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0y))@(ap@(c_2Ewords_2Edimword@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))) => ((p@(ap@(c_2Epred__set_2EFINITE@A_27a)@(c_2Epred__set_2EUNIV@A_27a))) => (((ap@(c_2Ewords_2En2w@A_27c)@(inj__ty_2Enum_2Enum @ V0y)) = (ap@(ap@(c_2Ewords_2Eword__concat@A_27a@A_27b@A_27c)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V1x)) <=> (V1x = (ap@(c_2Ewords_2En2w@A_27b)@(inj__ty_2Enum_2Enum @ V0y)))))))))))))).
thf(conj_thm_2EHolSmt_2Er244,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [A_27c:del]: ( ! [V0y:tp__ty_2Enum_2Enum] : ( ! [V1x:$i] : ((mem@V1x@(ty_2Efcp_2Ecart@bool@A_27b)) => ((p@(ap@(ap@c_2Earithmetic_2E_3C_3D@(ap@(c_2Efcp_2Edimindex@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))@(ap@(c_2Efcp_2Edimindex@A_27c)@(c_2Ebool_2Ethe__value@A_27c)))) => ((p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ V0y))@(ap@(c_2Ewords_2Edimword@A_27b)@(c_2Ebool_2Ethe__value@A_27b)))) => ((p@(ap@(c_2Epred__set_2EFINITE@A_27a)@(c_2Epred__set_2EUNIV@A_27a))) => (((ap@(c_2Ewords_2En2w@A_27c)@(inj__ty_2Enum_2Enum @ V0y)) = (ap@(ap@(c_2Ewords_2Eword__concat@A_27a@A_27b@A_27c)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V1x)) <=> ((ap@(c_2Ewords_2En2w@A_27b)@(inj__ty_2Enum_2Enum @ V0y)) = V1x)))))))))))).
thf(conj_thm_2EHolSmt_2Er245,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V0x)@V1y) = (ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V1y)@V0x)))))))).
thf(conj_thm_2EHolSmt_2Er246,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V2z:$i] : ((mem@V2z@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V0x)@(ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V1y)@V2z)) = (ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V1y)@(ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V0x)@V2z))))))))))).
thf(conj_thm_2EHolSmt_2Er247,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V2z:$i] : ((mem@V2z@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V0x)@(ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V1y)@V2z)) = (ap@(ap@(c_2Ewords_2Eword__and@A_27a)@(ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V0x)@V1y))@V2z)))))))))).
thf(conj_thm_2EHolSmt_2Er248,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1y:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(ap@(c_2Ewords_2Eword__and@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1y)))) <=> (((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0x) & ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V1y)))))).
thf(conj_thm_2EHolSmt_2Er249,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1y:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(ap@(c_2Ewords_2Eword__and@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1y)))) <=> (((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V1y) & ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0x)))))).
thf(stp_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))) => (X = (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(conj_thm_2EHolSmt_2Er250,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@(ap@(ap@(c_2Ewords_2Eword__extract@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))) = V0x))).
thf(conj_thm_2EHolSmt_2Er251,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@bool@A_27a)) => ((p@(ap@(ap@(c_2Ewords_2Eword__lo@A_27a)@V0x)@V1y)) <=> (~~ (p@(ap@(ap@(c_2Ewords_2Eword__ls@A_27a)@V1y)@V0x)))))))))).
thf(conj_thm_2EHolSmt_2Er252,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__mul@A_27a)@V0x)@V1y) = (ap@(ap@(c_2Ewords_2Eword__mul@A_27a)@V1y)@V0x)))))))).
thf(conj_thm_2EHolSmt_2Er253,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(ap@(ap@(c_2Ewords_2Eword__extract@ty_2Eone_2Eone@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))) = V0x))).
thf(conj_thm_2EHolSmt_2Er254,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V2z:$i] : ((mem@V2z@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__and@A_27a)@(ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V0x)@V1y))@V2z) = (ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V0x)@(ap@(ap@(c_2Ewords_2Eword__and@A_27a)@V1y)@V2z))))))))))).
thf(conj_thm_2EHolSmt_2Er255,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ((ap@(ap@(c_2Ewords_2Eword__or@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))@V0x) = V0x))))).
thf(conj_thm_2EHolSmt_2Et001,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ( ! [V2f:$i] : ((mem@V2f@(arr@A_27a@A_27b)) => ( ! [V3z:$i] : ((mem@V3z@A_27b) => ((V0x = V1y) | ((ap@V2f@V0x) = (ap@(ap@(ap@(ap@(c_2Ecombin_2EUPDATE@A_27a@A_27b)@V1y)@V3z)@V2f)@V0x)))))))))))))).
thf(conj_thm_2EHolSmt_2Et002,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ( ! [V2f:$i] : ((mem@V2f@(arr@A_27a@A_27b)) => ( ! [V3z:$i] : ((mem@V3z@A_27b) => ((V0x = V1y) | ((ap@V2f@V1y) = (ap@(ap@(ap@(ap@(c_2Ecombin_2EUPDATE@A_27a@A_27b)@V0x)@V3z)@V2f)@V1y)))))))))))))).
thf(conj_thm_2EHolSmt_2Et003,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ( ! [V2z:$i] : ((mem@V2z@A_27b) => ( ! [V3f:$i] : ((mem@V3f@(arr@A_27a@A_27b)) => ((V0x = V1y) | ((ap@(ap@(ap@(ap@(c_2Ecombin_2EUPDATE@A_27a@A_27b)@V1y)@V2z)@V3f)@V0x) = (ap@V3f@V0x)))))))))))))).
thf(conj_thm_2EHolSmt_2Et004,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0x:$i] : ((mem@V0x@A_27a) => ( ! [V1y:$i] : ((mem@V1y@A_27a) => ( ! [V2z:$i] : ((mem@V2z@A_27b) => ( ! [V3f:$i] : ((mem@V3f@(arr@A_27a@A_27b)) => ((V0x = V1y) | ((ap@(ap@(ap@(ap@(c_2Ecombin_2EUPDATE@A_27a@A_27b)@V0x)@V2z)@V3f)@V1y) = (ap@V3f@V1y)))))))))))))).
thf(conj_thm_2EHolSmt_2Et005,lemma,( ! [A_27a:del]: ( ! [A_27b:del]: ( ! [V0f:$i] : ((mem@V0f@(arr@A_27a@A_27b)) => ( ! [V1g:$i] : ((mem@V1g@(arr@A_27a@A_27b)) => ((V0f = V1g) | (~~ ((ap@V0f@(ap@(ap@(c_2EHolSmt_2Earray__ext@A_27a@A_27b)@V0f)@V1g)) = (ap@V1g@(ap@(ap@(c_2EHolSmt_2Earray__ext@A_27a@A_27b)@V0f)@V1g)))))))))))).
thf(conj_thm_2EHolSmt_2Et006,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((~~ (V0x = V1y)) | (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))))))).
thf(conj_thm_2EHolSmt_2Et007,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((~~ (V0x = V1y)) | (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))))))).
thf(conj_thm_2EHolSmt_2Et008,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((~~ (V0x = V1y)) | (p@(ap@(ap@c_2Einteger_2Eint__ge@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Et009,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((~~ (V0x = V1y)) | (p@(ap@(ap@c_2Einteger_2Eint__le@(ap@(ap@c_2Einteger_2Eint__add@(inj__ty_2Einteger_2Eint @ V0x))@(ap@(ap@c_2Einteger_2Eint__mul@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Einteger_2Eint @ V1y))))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Et010,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((V0x = V1y) | ((~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y)))) | (~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))))))))).
thf(conj_thm_2EHolSmt_2Et011,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) | (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))).
thf(conj_thm_2EHolSmt_2Et012,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))) | (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2EHolSmt_2Et013,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) | (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))).
thf(conj_thm_2EHolSmt_2Et014,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ((~~ (p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))) | (~~ (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(ap@c_2Einteger_2Eint__neg@(ap@c_2Einteger_2Eint__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))).
thf(conj_thm_2EHolSmt_2Et015,lemma,( ! [V0x:tp__ty_2Einteger_2Eint] : ( ! [V1y:tp__ty_2Einteger_2Eint] : ((p@(ap@(ap@c_2Einteger_2Eint__ge@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))) | (p@(ap@(ap@c_2Einteger_2Eint__le@(inj__ty_2Einteger_2Eint @ V0x))@(inj__ty_2Einteger_2Eint @ V1y))))))).
thf(conj_thm_2EHolSmt_2Et016,lemma,( ! [V0x:tp__ty_2Erealax_2Ereal] : ( ! [V1y:tp__ty_2Erealax_2Ereal] : ((~~ (V0x = V1y)) | (p@(ap@(ap@c_2Ereal_2Ereal__ge@(ap@(ap@c_2Erealax_2Ereal__add@(inj__ty_2Erealax_2Ereal @ V0x))@(ap@(ap@c_2Erealax_2Ereal__mul@(ap@c_2Erealax_2Ereal__neg@(ap@c_2Ereal_2Ereal__of__num@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))@(inj__ty_2Erealax_2Ereal @ V1y))))@(ap@c_2Ereal_2Ereal__of__num@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))).
thf(conj_thm_2EHolSmt_2Et017,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => (~~ (V0x = (ap@(c_2Ewords_2Eword__1comp@A_27a)@V0x))))))).
thf(conj_thm_2EHolSmt_2Et018,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V2i:tp__ty_2Enum_2Enum] : ((V0x = V1y) => ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@V0x)@(inj__ty_2Enum_2Enum @ V2i))) => (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@V1y)@(inj__ty_2Enum_2Enum @ V2i)))))))))))).
thf(conj_thm_2EHolSmt_2Et019,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2Eword__1comp@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x)))) | (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))).
thf(conj_thm_2EHolSmt_2Et020,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2Eword__1comp@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))))))).
thf(conj_thm_2EHolSmt_2Et021,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0x)))).
thf(conj_thm_2EHolSmt_2Et022,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ((~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V0x)))).
thf(conj_thm_2EHolSmt_2Et023,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ((~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) => ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2Eword__1comp@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))))))).
thf(conj_thm_2EHolSmt_2Et024,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2Eword__1comp@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x)))) | (~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2EHolSmt_2Et025,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1y:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(ap@(c_2Ewords_2Eword__or@ty_2Eone_2Eone)@(ap@(c_2Ewords_2Eword__1comp@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x)))@(ap@(c_2Ewords_2Eword__1comp@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1y))))) | (~~ ((~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) | (~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@ty_2Eone_2Eone)@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V1y))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2EHolSmt_2Et026,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = V0x) | ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) | ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) | ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) | ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) | ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) | ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) | ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) | (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))))))).
thf(conj_thm_2EHolSmt_2Et027,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1p:$i] : ((mem@V1p@bool) => (((V0x = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))) <=> (p@V1p)) <=> (V0x = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@V1p)@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2EHolSmt_2Et028,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : ( ! [V1p:$i] : ((mem@V1p@bool) => ((((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0x) <=> (p@V1p)) <=> (V0x = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@V1p)@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2EHolSmt_2Et029,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (((p@V0p) <=> (V1x = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))) <=> (V1x = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@V0p)@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(conj_thm_2EHolSmt_2Et030,lemma,( ! [V0p:$i] : ((mem@V0p@bool) => ( ! [V1x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (((p@V0p) <=> ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V1x)) <=> (V1x = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(ap@(ap@(c_2Ebool_2ECOND@(ty_2Efcp_2Ecart@bool@ty_2Eone_2Eone))@V0p)@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@(ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))).
thf(stp_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : $tType)).
thf(stp_inj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : (tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone > $i))).
thf(stp_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,type,(surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone : ($i > tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone))).
thf(stp_inj_surj_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : ((surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)) = X))).
thf(stp_inj_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (mem @ (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X) @ (ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))))).
thf(stp_iso_mem_c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone,axiom,( ! [X:$i] : ((mem @ X @ (ty_2Efcp_2Ecart@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))) => (X = (inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ X)))))).
thf(conj_thm_2EHolSmt_2Et031,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@(ap@(c_2Ewords_2Eword__mul@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(ap@(c_2Ewords_2En2w@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))))))))))))))))))))))))))@(ap@(c_2Ewords_2Esw2sw@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))))) => (~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))).
thf(conj_thm_2EHolSmt_2Et032,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@(ap@(c_2Ewords_2Eword__mul@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(ap@(c_2Ewords_2En2w@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))))))))))))))))))))))))))@(ap@(c_2Ewords_2Esw2sw@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))))) => (~~ ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> (~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))))).
thf(conj_thm_2EHolSmt_2Et033,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = (surj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ (ap@(ap@(c_2Ewords_2Eword__mul@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(ap@(c_2Ewords_2En2w@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))))))))))))))))))))))))))))))))))@(ap@(c_2Ewords_2Esw2sw@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))))) => (~~ ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT2@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) <=> ((~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) & (~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(inj__c_ty_2Efcp_2Ecart_o_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_c_ty_2Efcp_2Ebit0_ty_2Eone_2Eone @ V0x))@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))))).
thf(conj_thm_2EHolSmt_2Et034,lemma,( ! [A_27a:del]: ( ! [V0x:$i] : ((mem@V0x@(ty_2Efcp_2Ecart@bool@A_27a)) => ( ! [V1y:$i] : ((mem@V1y@(ty_2Efcp_2Ecart@bool@A_27a)) => (((ap@(ap@(c_2Ewords_2Eword__add@A_27a)@(ap@(c_2Ewords_2En2w@A_27a)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))@V0x) = V1y) => ((p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@V0x)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) => (~~ (p@(ap@(ap@(c_2Efcp_2Efcp__index@bool@A_27a)@V1y)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))))))).
thf(conj_thm_2EHolSmt_2Et035,lemma,( ! [V0x:tp__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone] : (((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))) = V0x) | (~~ ((surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(ap@(ap@(c_2Ewords_2Eword__extract@ty_2Eone_2Eone@ty_2Eone_2Eone)@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(inj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ V0x))) = (surj__c_ty_2Efcp_2Ecart_o_ty_2Eone_2Eone @ (ap@(c_2Ewords_2En2w@ty_2Eone_2Eone)@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))).
thf(conj_thm_2EHolSmt_2Ep001,lemma,( ! [A_27a:del]: (p@(ap@(ap@c_2Eprim__rec_2E_3C@(inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))).
thf(conj_thm_2EHolSmt_2Ep002,lemma,( ! [A_27a:del]: (p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO))))@(ap@(c_2Ewords_2Edimword@A_27a)@(c_2Ebool_2Ethe__value@A_27a)))))).
thf(conj_thm_2EHolSmt_2Ep003,lemma,(p@(ap@(ap@c_2Eprim__rec_2E_3C@(ap@c_2Earithmetic_2ENUMERAL@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(ap@c_2Earithmetic_2EBIT1@(inj__ty_2Enum_2Enum @ fo__c_2Earithmetic_2EZERO)))))))))))@(ap@(c_2Ewords_2Edimword@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone))))@(c_2Ebool_2Ethe__value@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))))).
thf(conj_thm_2EHolSmt_2Ep004,lemma,(p@(ap@(c_2Epred__set_2EFINITE@ty_2Eone_2Eone)@(c_2Epred__set_2EUNIV@ty_2Eone_2Eone)))).
thf(conj_thm_2EHolSmt_2Ep005,lemma,(p@(ap@(c_2Epred__set_2EFINITE@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))@(c_2Epred__set_2EUNIV@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@ty_2Eone_2Eone)))))))).
thf(conj_thm_2EHolSmt_2Ep006,lemma,(p@(ap@(c_2Epred__set_2EFINITE@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit1@ty_2Eone_2Eone)))))@(c_2Epred__set_2EUNIV@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit1@ty_2Eone_2Eone)))))))).
thf(conj_thm_2EHolSmt_2Ep007,conjecture,(p@(ap@(c_2Epred__set_2EFINITE@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@ty_2Eone_2Eone)))))@(c_2Epred__set_2EUNIV@(ty_2Efcp_2Ebit0@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@(ty_2Efcp_2Ebit1@ty_2Eone_2Eone)))))))).
