--- a/src/HOL/Computational_Algebra/Polynomial.thy Sun Mar 22 17:21:16 2020 +0000
+++ b/src/HOL/Computational_Algebra/Polynomial.thy Sun Mar 22 19:02:39 2020 +0000
@@ -4367,11 +4367,11 @@
define m where "m = (GREATEST m. \<not>c dvd coeff b m)"
assume "\<not>[:c:] dvd b"
hence A: "\<exists>i. \<not>c dvd coeff b i" by (subst (asm) const_poly_dvd_iff) blast
- have B: "\<forall>i. \<not>c dvd coeff b i \<longrightarrow> i \<le> degree b"
+ have B: "\<And>i. \<not>c dvd coeff b i \<Longrightarrow> i \<le> degree b"
by (auto intro: le_degree)
have coeff_m: "\<not>c dvd coeff b m" unfolding m_def by (rule GreatestI_ex_nat[OF A B])
have "i \<le> m" if "\<not>c dvd coeff b i" for i
- unfolding m_def by (rule Greatest_le_nat[OF that B])
+ unfolding m_def by (metis (mono_tags, lifting) B Greatest_le_nat that)
hence dvd_b: "c dvd coeff b i" if "i > m" for i using that by force
have "c dvd coeff a i" for i
--- a/src/HOL/Computational_Algebra/Polynomial_Factorial.thy Sun Mar 22 17:21:16 2020 +0000
+++ b/src/HOL/Computational_Algebra/Polynomial_Factorial.thy Sun Mar 22 19:02:39 2020 +0000
@@ -286,11 +286,11 @@
define m where "m = (GREATEST m. \<not>c dvd coeff b m)"
assume "\<not>[:c:] dvd b"
hence A: "\<exists>i. \<not>c dvd coeff b i" by (subst (asm) const_poly_dvd_iff) blast
- have B: "\<forall>i. \<not>c dvd coeff b i \<longrightarrow> i \<le> degree b"
+ have B: "\<And>i. \<not>c dvd coeff b i \<Longrightarrow> i \<le> degree b"
by (auto intro: le_degree)
have coeff_m: "\<not>c dvd coeff b m" unfolding m_def by (rule GreatestI_ex_nat[OF A B])
have "i \<le> m" if "\<not>c dvd coeff b i" for i
- unfolding m_def by (rule Greatest_le_nat[OF that B])
+ unfolding m_def by (blast intro!: Greatest_le_nat that B)
hence dvd_b: "c dvd coeff b i" if "i > m" for i using that by force
have "c dvd coeff a i" for i