equal
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367 interpret normed_vectorspace_with_fn_norm [E norm B fn_norm] |
367 interpret normed_vectorspace_with_fn_norm [E norm B fn_norm] |
368 by (auto simp: B_def fn_norm_def) intro_locales |
368 by (auto simp: B_def fn_norm_def) intro_locales |
369 interpret subspace [F E] by fact |
369 interpret subspace [F E] by fact |
370 interpret linearform [F f] by fact |
370 interpret linearform [F f] by fact |
371 interpret continuous [F norm f] by fact |
371 interpret continuous [F norm f] by fact |
372 have E: "vectorspace E" by unfold_locales |
372 have E: "vectorspace E" by intro_locales |
373 have F: "vectorspace F" by rule unfold_locales |
373 have F: "vectorspace F" by rule intro_locales |
374 have F_norm: "normed_vectorspace F norm" |
374 have F_norm: "normed_vectorspace F norm" |
375 using FE E_norm by (rule subspace_normed_vs) |
375 using FE E_norm by (rule subspace_normed_vs) |
376 have ge_zero: "0 \<le> \<parallel>f\<parallel>\<hyphen>F" |
376 have ge_zero: "0 \<le> \<parallel>f\<parallel>\<hyphen>F" |
377 by (rule normed_vectorspace_with_fn_norm.fn_norm_ge_zero |
377 by (rule normed_vectorspace_with_fn_norm.fn_norm_ge_zero |
378 [OF normed_vectorspace_with_fn_norm.intro, |
378 [OF normed_vectorspace_with_fn_norm.intro, |