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-family-and-montel-theorem->residue-theorem","source":"normal-family-and-montel-theorem","target":"residue-theorem","relation":"uses","crossDomain":false},{"id":"requires:regular-value->regular-level-set-theorem","source":"regular-value","target":"regular-level-set-theorem","relation":"requires","crossDomain":false},{"id":"uses:regular-level-set-theorem->constant-rank-theorem","source":"regular-level-set-theorem","target":"constant-rank-theorem","relation":"uses","crossDomain":false},{"id":"requires:regular-language->pumping-lemma-regular","source":"regular-language","target":"pumping-lemma-regular","relation":"requires","crossDomain":false},{"id":"uses:pumping-lemma-regular->pigeonhole-principle","source":"pumping-lemma-regular","target":"pigeonhole-principle","relation":"uses","crossDomain":true},{"id":"requires:regular-language->closure-properties-regular-languages","source":"regular-language","target":"closure-properties-regular-languages","relation":"requires","crossDomain":false},{"id":"requires:language-operations->closure-properties-regular-languages","source":"language-operations","target":"closure-properties-regular-languages","relation":"requires","crossDomain":false},{"id":"uses:closure-properties-regular-languages->dfa-nfa-equivalence","source":"closure-properties-regular-languages","target":"dfa-nfa-equivalence","relation":"uses","crossDomain":false},{"id":"requires:bayesian-statistical-model->evidence-lower-bound","source":"bayesian-statistical-model","target":"evidence-lower-bound","relation":"requires","crossDomain":false},{"id":"uses:evidence-lower-bound->jensen-inequality","source":"evidence-lower-bound","target":"jensen-inequality","relation":"uses","crossDomain":true},{"id":"uses:evidence-lower-bound->kl-divergence","source":"evidence-lower-bound","target":"kl-divergence","relation":"uses","crossDomain":true},{"id":"requires:rank-of-linear-map->rank-nullity-theorem","source":"rank-of-linear-map","target":"rank-nullity-theorem","relation":"requires","crossDomain":false},{"id":"requires:confidence-interval->confidence-set-test-duality","source":"confidence-interval","target":"confidence-set-test-duality","relation":"requires","crossDomain":false},{"id":"requires:statistical-hypothesis-test->confidence-set-test-duality","source":"statistical-hypothesis-test","target":"confidence-set-test-duality","relation":"requires","crossDomain":false},{"id":"requires:independence->central-limit-theorem","source":"independence","target":"central-limit-theorem","relation":"requires","crossDomain":false},{"id":"requires:variance->central-limit-theorem","source":"variance","target":"central-limit-theorem","relation":"requires","crossDomain":false},{"id":"requires:convergence-in-distribution->central-limit-theorem","source":"convergence-in-distribution","target":"central-limit-theorem","relation":"requires","crossDomain":false},{"id":"requires:normal-distribution->central-limit-theorem","source":"normal-distribution","target":"central-limit-theorem","relation":"requires","crossDomain":false},{"id":"contrasts_with:central-limit-theorem->hoeffding-inequality","source":"central-limit-theorem","target":"hoeffding-inequality","relation":"contrasts_with","crossDomain":false},{"id":"contrasts_with:central-limit-theorem->law-of-large-numbers","source":"central-limit-theorem","target":"law-of-large-numbers","relation":"contrasts_with","crossDomain":false},{"id":"requires:derivative->mean-value-theorem","source":"derivative","target":"mean-value-theorem","relation":"requires","crossDomain":false},{"id":"requires:continuity->mean-value-theorem","source":"continuity","target":"mean-value-theorem","relation":"requires","crossDomain":false},{"id":"uses:mean-value-theorem->extreme-value-theorem","source":"mean-value-theorem","target":"extreme-value-theorem","relation":"uses","crossDomain":false},{"id":"requires:asymptotic-notation->master-theorem","source":"asymptotic-notation","target":"master-theorem","relation":"requires","crossDomain":false},{"id":"uses:master-theorem->divide-and-conquer","source":"master-theorem","target":"divide-and-conquer","relation":"uses","crossDomain":false},{"id":"requires:class-p-poly->natural-proofs-barrier","source":"class-p-poly","target":"natural-proofs-barrier","relation":"requires","crossDomain":false},{"id":"requires:pseudorandom-function->natural-proofs-barrier","source":"pseudorandom-function","target":"natural-proofs-barrier","relation":"requires","crossDomain":true},{"id":"contrasts_with:natural-proofs-barrier->razborov-approximation-method","source":"natural-proofs-barrier","target":"razborov-approximation-method","relation":"contrasts_with","crossDomain":false},{"id":"requires:set-construction-combinatorics->exponential-formula-combinatorics","source":"set-construction-combinatorics","target":"exponential-formula-combinatorics","relation":"requires","crossDomain":false},{"id":"requires:labeled-combinatorial-class->exponential-formula-combinatorics","source":"labeled-combinatorial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