src/HOL/Algebra/Divisibility.thy
changeset 39302 d7728f65b353
parent 36903 489c1fbbb028
child 41413 64cd30d6b0b8
equal deleted inserted replaced
39301:e1bd8a54c40f 39302:d7728f65b353
  2191       and csf: "wfactors G cs c"
  2191       and csf: "wfactors G cs c"
  2192       and csmset: "fmset G cs = fmset G bs - fmset G as" by auto
  2192       and csmset: "fmset G cs = fmset G bs - fmset G as" by auto
  2193 
  2193 
  2194   from csmset msubset
  2194   from csmset msubset
  2195       have "fmset G bs = fmset G as + fmset G cs"
  2195       have "fmset G bs = fmset G as + fmset G cs"
  2196       by (simp add: multiset_ext_iff mset_le_def)
  2196       by (simp add: multiset_eq_iff mset_le_def)
  2197   hence basc: "b \<sim> a \<otimes> c"
  2197   hence basc: "b \<sim> a \<otimes> c"
  2198       by (rule fmset_wfactors_mult) fact+
  2198       by (rule fmset_wfactors_mult) fact+
  2199 
  2199 
  2200   thus ?thesis
  2200   thus ?thesis
  2201   proof (elim associatedE2)
  2201   proof (elim associatedE2)