src/HOL/Real/HahnBanach/HahnBanach.thy
changeset 14291 61df18481f53
parent 14214 5369d671f100
child 14334 6137d24eef79
equal deleted inserted replaced
14290:84fda1b39947 14291:61df18481f53
   338   have E_norm: "normed_vectorspace E norm" ..
   338   have E_norm: "normed_vectorspace E norm" ..
   339   have FE: "F \<unlhd> E" .
   339   have FE: "F \<unlhd> E" .
   340   have F: "vectorspace F" ..
   340   have F: "vectorspace F" ..
   341   have linearform: "linearform F f" .
   341   have linearform: "linearform F f" .
   342   have F_norm: "normed_vectorspace F norm"
   342   have F_norm: "normed_vectorspace F norm"
   343     by (rule subspace_normed_vs [OF _ _ _ norm.intro])
   343     by (rule subspace_normed_vs [OF _ _ norm.intro])
   344   have ge_zero: "0 \<le> \<parallel>f\<parallel>\<hyphen>F"
   344   have ge_zero: "0 \<le> \<parallel>f\<parallel>\<hyphen>F"
   345     by (rule normed_vectorspace.fn_norm_ge_zero
   345     by (rule normed_vectorspace.fn_norm_ge_zero
   346       [OF F_norm _ continuous.intro, folded B_def fn_norm_def])
   346       [OF F_norm _ continuous.intro, folded B_def fn_norm_def])
   347 
   347 
   348   txt {* We define a function @{text p} on @{text E} as follows:
   348   txt {* We define a function @{text p} on @{text E} as follows: