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281 |
281 |
282 |
282 |
283 subsection{*Additive Inverse on Nonstandard Complex Numbers*} |
283 subsection{*Additive Inverse on Nonstandard Complex Numbers*} |
284 |
284 |
285 lemma hcomplex_minus_congruent: |
285 lemma hcomplex_minus_congruent: |
286 "congruent hcomplexrel (%X. hcomplexrel `` {%n. - (X n)})" |
286 "(%X. hcomplexrel `` {%n. - (X n)}) respects hcomplexrel" |
287 by (simp add: congruent_def) |
287 by (simp add: congruent_def) |
288 |
288 |
289 lemma hcomplex_minus: |
289 lemma hcomplex_minus: |
290 "- (Abs_hcomplex(hcomplexrel `` {%n. X n})) = |
290 "- (Abs_hcomplex(hcomplexrel `` {%n. X n})) = |
291 Abs_hcomplex(hcomplexrel `` {%n. -(X n)})" |
291 Abs_hcomplex(hcomplexrel `` {%n. -(X n)})" |