src/HOL/Hyperreal/MacLaurin.thy
changeset 15229 1eb23f805c06
parent 15140 322485b816ac
child 15234 ec91a90c604e
equal deleted inserted replaced
15228:4d332d10fa3d 15229:1eb23f805c06
   326                      (diff n t / real (fact n)) * x ^ n"
   326                      (diff n t / real (fact n)) * x ^ n"
   327 apply (rule_tac x = x and y = 0 in linorder_cases)
   327 apply (rule_tac x = x and y = 0 in linorder_cases)
   328 prefer 2 apply blast
   328 prefer 2 apply blast
   329 apply (drule_tac [2] diff=diff in Maclaurin)
   329 apply (drule_tac [2] diff=diff in Maclaurin)
   330 apply (drule_tac diff=diff in Maclaurin_minus, simp_all, safe)
   330 apply (drule_tac diff=diff in Maclaurin_minus, simp_all, safe)
   331 apply (rule_tac [!] x = t in exI, auto, arith+)
   331 apply (rule_tac [!] x = t in exI, auto)
   332 done
   332 done
   333 
   333 
   334 lemma Maclaurin_all_lt_objl:
   334 lemma Maclaurin_all_lt_objl:
   335      "diff 0 = f &
   335      "diff 0 = f &
   336       (\<forall>m x. DERIV (diff m) x :> diff(Suc m) x) &
   336       (\<forall>m x. DERIV (diff m) x :> diff(Suc m) x) &