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6 | 6 |
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7 | 7 | - in `realfun.v`: |
8 | 8 | + lemma `derivable_sqrt` |
9 | | -- in `topology_structure.v` |
10 | | - + lemma `interiorS` |
11 | | - |
12 | | -- in `order_topology.v` |
13 | | - + lemma `itv_closed_ends_closed` |
14 | | -- in `classical_sets.v` |
15 | | - + lemma `in_set1_eq` |
16 | | - |
17 | | -- in `set_interval.v` |
18 | | - + definitions `itv_is_closed_unbounded`, `itv_is_cc`, `itv_closed_ends` |
19 | | - |
20 | | -- in `Rstruct.v`: |
21 | | - + lemmas `R0E` and `R1E` |
22 | | - + multirule `RealsE` to convert from Stdlib reals to Analysis ones |
23 | | - |
24 | | -- in `Rstruct_topology.v`: |
25 | | - + lemma `RlnE` |
26 | | -- in probability.v |
27 | | - + lemma `pmf_ge0` |
28 | | - + lemmas `pmf_gt0_countable`, `pmf_measurable` |
29 | | - |
30 | | -- in `unstable.v`: |
31 | | - + lemmas `oppr_itvNy`, `oppr_itvy` |
32 | | - + lemmas `ltr_norm_bound`, `real_ltr_bound`, `real_ltrNbound`, `ltr_bound`, |
33 | | - `ltrNbound` |
34 | | - |
35 | | -- in `set_interval.v`: |
36 | | - + lemmas `opp_preimage_itvbndy`, `opp_preimage_itvbndbnd` |
37 | | - |
38 | | -- in `lebesgue_measure.v`: |
39 | | - + lemma `lebesgue_measure_unique` |
40 | | - |
41 | | -- in `lebesgue_integral_nonneg.v`: |
42 | | - + lemmas `lebesgue_measureN`, `ge0_integration_by_substitution0` |
43 | | - |
44 | | -- in `measurable_realfun.v`: |
45 | | - + definition `min_mfun` |
46 | | - |
47 | | -- in `random_variable.v` |
48 | | - + lemmas `lebesgue_integral_pmf`, `cdf_measurable`, `ccdf_measurable`, |
49 | | - `le0_expectation_cdf` |
50 | | - |
51 | | -- in `lebesgue_integral_nonneg.v`: |
52 | | - + lemma `integral_setU` |
53 | | - |
54 | | -- in `measurable_realfun.v`: |
55 | | - + lemmas `emeasurable_fun_itv_obnd_cbndP`, `emeasurable_fun_itv_bndo_bndcP`, |
56 | | - `emeasurable_fun_itv_cc` |
57 | | -- in `derive.v`: |
58 | | - + lemmas `derivable_mxP`, `derive_mx` |
59 | | - |
60 | | -- in `subtype_topology.v`: |
61 | | - + lemma `within_continuous_comp` |
62 | | - |
63 | | -- in `pseudometric_normed_Zmodule.v`: |
64 | | - + lemmas `within_continuousB`, `within_continuousD` |
65 | | - |
66 | | -- in `normed_module.v`: |
67 | | - + lemma `within_continuous_compN` |
68 | | -- in `normed_module.v`: |
69 | | - + lemma `compact_has_sup` |
70 | | - |
71 | | -- in `derive.v`: |
72 | | - + lemmas `compact_EVT_max`, `compact_EVT_min`, `EVT_max_rV`, `EVT_min_rV` |
73 | | -- in `tvs.v` |
74 | | - + lemmas `cvg_sum`, `sum_continuous` |
75 | 9 |
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76 | 10 | - in `unstable.v`: |
77 | 11 | + structure `Norm` |
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