equal
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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: |