equal
deleted
inserted
replaced
193 apply (drule_tac x = "epsilon / 2" in spec) |
193 apply (drule_tac x = "epsilon / 2" in spec) |
194 using egt0 unfolding mult.commute [of 2] by force |
194 using egt0 unfolding mult.commute [of 2] by force |
195 then obtain a' where a'lea [arith]: "a' > a" and |
195 then obtain a' where a'lea [arith]: "a' > a" and |
196 a_prop: "F a' - F a < epsilon / 2" |
196 a_prop: "F a' - F a < epsilon / 2" |
197 by auto |
197 by auto |
198 def S' \<equiv> "{i. l i < r i}" |
198 define S' where "S' = {i. l i < r i}" |
199 obtain S :: "nat set" where |
199 obtain S :: "nat set" where |
200 "S \<subseteq> S'" and finS: "finite S" and |
200 "S \<subseteq> S'" and finS: "finite S" and |
201 Sprop: "{a'..b} \<subseteq> (\<Union>i \<in> S. {l i<..<r i + delta i})" |
201 Sprop: "{a'..b} \<subseteq> (\<Union>i \<in> S. {l i<..<r i + delta i})" |
202 proof (rule compactE_image) |
202 proof (rule compactE_image) |
203 show "compact {a'..b}" |
203 show "compact {a'..b}" |