less: fixes a' :: "real"   and b' :: "real"   and a :: "(real \<times> real \<times> real) list"   and c' :: "real"   and x :: "real"   and b :: "(real \<times> real \<times> real) list"   and c :: "(real \<times> real \<times> real) list"   and d :: "(real \<times> real \<times> real) list" shows "((a' = 0 \<and> b' \<noteq> 0) \<and> (\<forall>(d, e, f)\<in>set a. evalUni (substInfinitesimalLinearUni b' c' (EqUni (d, e, f))) x) \<and> (\<forall>(d, e, f)\<in>set b. evalUni (substInfinitesimalLinearUni b' c' (LessUni (d, e, f))) x) \<and> (\<forall>(d, e, f)\<in>set c. evalUni (substInfinitesimalLinearUni b' c' (LeqUni (d, e, f))) x) \<and> (\<forall>(d, e, f)\<in>set d. evalUni (substInfinitesimalLinearUni b' c' (NeqUni (d, e, f))) x) \<or> a' \<noteq> 0 \<and> - b'\<^sup>2 + 4 * a' * c' \<le> 0 \<and> ((\<forall>(d, e, f)\<in>set a. evalUni (substInfinitesimalQuadraticUni (- b') 1 (b'\<^sup>2 - 4 * a' * c') (2 * a') (EqUni (d, e, f))) x) \<and> (\<forall>(d, e, f)\<in>set b. evalUni (substInfinitesimalQuadraticUni (- b') 1 (b'\<^sup>2 - 4 * a' * c') (2 * a') (LessUni (d, e, f))) x) \<and> (\<forall>(d, e, f)\<in>set c. evalUni (substInfinitesimalQuadraticUni (- b') 1 (b'\<^sup>2 - 4 * a' * c') (2 * a') (LeqUni (d, e, f))) x) \<and> (\<forall>(d, e, f)\<in>set d. evalUni (substInfinitesimalQuadraticUni (- b') 1 (b'\<^sup>2 - 4 * a' * c') (2 * a') (NeqUni (d, e, f))) x) \<or> (\<forall>(d, e, f)\<in>set a. evalUni (substInfinitesimalQuadraticUni (- b') (- 1) (b'\<^sup>2 - 4 * a' * c') (2 * a') (EqUni (d, e, f))) x) \<and> (\<forall>(d, e, f)\<in>set b. evalUni (substInfinitesimalQuadraticUni (- b') (- 1) (b'\<^sup>2 - 4 * a' * c') (2 * a') (LessUni (d, e, f))) x) \<and> (\<forall>(d, e, f)\<in>set c. evalUni (substInfinitesimalQuadraticUni (- b') (- 1) (b'\<^sup>2 - 4 * a' * c') (2 * a') (LeqUni (d, e, f))) x) \<and> (\<forall>(d, e, f)\<in>set d. evalUni (substInfinitesimalQuadraticUni (- b') (- 1) (b'\<^sup>2 - 4 * a' * c') (2 * a') (NeqUni (d, e, f))) x))) = ((a' = 0 \<and> b' \<noteq> 0) \<and> (\<forall>(d, e, f)\<in>set a. \<exists>y'>- c' / b'. \<forall>x\<in>{- c' / b'<..y'}. aEvalUni (EqUni (d, e, f)) x) \<and> (\<forall>(d, e, f)\<in>set b. \<exists>y'>- c' / b'. \<forall>x\<in>{- c' / b'<..y'}. aEvalUni (LessUni (d, e, f)) x) \<and> (\<forall>(d, e, f)\<in>set c. \<exists>y'>- c' / b'. \<forall>x\<in>{- c' / b'<..y'}. aEvalUni (LeqUni (d, e, f)) x) \<and> (\<forall>(d, e, f)\<in>set d. \<exists>y'>- c' / b'. \<forall>x\<in>{- c' / b'<..y'}. aEvalUni (NeqUni (d, e, f)) x) \<or> a' \<noteq> 0 \<and> - b'\<^sup>2 + 4 * a' * c' \<le> 0 \<and> ((\<forall>(d, e, f)\<in>set a. \<exists>y'>(- b' + 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a'). \<forall>x\<in>{(- b' + 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a')<..y'}. aEvalUni (EqUni (d, e, f)) x) \<and> (\<forall>(d, e, f)\<in>set b. \<exists>y'>(- b' + 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a'). \<forall>x\<in>{(- b' + 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a')<..y'}. aEvalUni (LessUni (d, e, f)) x) \<and> (\<forall>(d, e, f)\<in>set c. \<exists>y'>(- b' + 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a'). \<forall>x\<in>{(- b' + 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a')<..y'}. aEvalUni (LeqUni (d, e, f)) x) \<and> (\<forall>(d, e, f)\<in>set d. \<exists>y'>(- b' + 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a'). \<forall>x\<in>{(- b' + 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a')<..y'}. aEvalUni (NeqUni (d, e, f)) x) \<or> (\<forall>(d, e, f)\<in>set a. \<exists>y'>(- b' + - 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a'). \<forall>x\<in>{(- b' + - 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a')<..y'}. aEvalUni (EqUni (d, e, f)) x) \<and> (\<forall>(d, e, f)\<in>set b. \<exists>y'>(- b' + - 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a'). \<forall>x\<in>{(- b' + - 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a')<..y'}. aEvalUni (LessUni (d, e, f)) x) \<and> (\<forall>(d, e, f)\<in>set c. \<exists>y'>(- b' + - 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a'). \<forall>x\<in>{(- b' + - 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a')<..y'}. aEvalUni (LeqUni (d, e, f)) x) \<and> (\<forall>(d, e, f)\<in>set d. \<exists>y'>(- b' + - 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a'). \<forall>x\<in>{(- b' + - 1 * sqrt (b'\<^sup>2 - 4 * a' * c')) / (2 * a')<..y'}. aEvalUni (NeqUni (d, e, f)) x)))"