elims_1: fixes x :: "nat"   and xa :: "floatarith"   and xb :: "real list"   and y :: "bool" assumes "isDERIV x xa xb = y" obtains xc :: "nat" and a :: "floatarith" and b :: "floatarith" and vs :: "real list" where "x = xc__" and "xa = Add a__ b__" and "xb = vs__" and "y = (isDERIV xc__ a__ vs__ \<and> isDERIV xc__ b__ vs__)"   | xc :: "nat" and a :: "floatarith" and b :: "floatarith" and vs :: "real list" where "x = xca__" and "xa = Mult aa__ ba__" and "xb = vsa__" and "y = (isDERIV xca__ aa__ vsa__ \<and> isDERIV xca__ ba__ vsa__)"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xcb__" and "xa = Minus ab__" and "xb = vsb__" and "y = isDERIV xcb__ ab__ vsb__"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xcc__" and "xa = Inverse ac__" and "xb = vsc__" and "y = (isDERIV xcc__ ac__ vsc__ \<and> interpret_floatarith ac__ vsc__ \<noteq> 0)"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xcd__" and "xa = Cos ad__" and "xb = vsd__" and "y = isDERIV xcd__ ad__ vsd__"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xce__" and "xa = Arctan ae__" and "xb = vse__" and "y = isDERIV xce__ ae__ vse__"   | xc :: "nat" and a :: "floatarith" and b :: "floatarith" and vs :: "real list" where "x = xcf__" and "xa = Min af__ bb__" and "xb = vsf__" and "\<not> y"   | xc :: "nat" and a :: "floatarith" and b :: "floatarith" and vs :: "real list" where "x = xcg__" and "xa = Max ag__ bc__" and "xb = vsg__" and "\<not> y"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xch__" and "xa = Abs ah__" and "xb = vsh__" and "\<not> y"   | xc :: "nat" and vs :: "real list" where "x = xci__" and "xa = Pi" and "xb = vsi__" and "y"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xcj__" and "xa = Sqrt ai__" and "xb = vsj__" and "y = (isDERIV xcj__ ai__ vsj__ \<and> 0 < interpret_floatarith ai__ vsj__)"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xck__" and "xa = Exp aj__" and "xb = vsk__" and "y = isDERIV xck__ aj__ vsk__"   | xc :: "nat" and a :: "floatarith" and b :: "floatarith" and vs :: "real list" where "x = xcl__" and "xa = Powr ak__ b" and "xb = vsl__" and "y = (isDERIV xcl__ ak__ vsl__ \<and> isDERIV xcl__ b vsl__ \<and> 0 < interpret_floatarith ak__ vsl__)"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xcm__" and "xa = Ln al__" and "xb = vsm__" and "y = (isDERIV xcm__ al__ vsm__ \<and> 0 < interpret_floatarith al__ vsm__)"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xcn__" and "xa = Floor am__" and "xb = vsn__" and "y = (isDERIV xcn__ am__ vsn__ \<and> interpret_floatarith am__ vsn__ \<notin> \<int>)"   | xc :: "nat" and a :: "floatarith" and vs :: "real list" where "x = xco__" and "xa = an__ ^\<^sub>e 0" and "xb = vso__" and "y"   | xc :: "nat" and a :: "floatarith" and n :: "nat" and vs :: "real list" where "x = xcp__" and "xa = a ^\<^sub>e Suc n__" and "xb = vsp__" and "y = isDERIV xcp__ a vsp__"   | xc :: "nat" and f :: "float" and vs :: "real list" where "x = xcq__" and "xa = Num f" and "xb = vsq__" and "y"   | xc :: "nat" and n :: "nat" and vs :: "real list" where "x = xc" and "xa = Var n" and "xb = vs" and "y"