two lemmas from infotheo #406
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CohenCyril
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Jul 13, 2021
CohenCyril
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Jul 13, 2021
theories/classical_sets.v
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| Lemma bigcup_of_set1 {rT I} (P : set I) (f : I -> rT) : | ||
| \bigcup_(x in P) [set f x] = f @` P. | ||
| Proof. | ||
| by rewrite eqEsubset; split=> [a [i ?]->| a [i ?]<-]; [apply imageP | exists i]. |
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| by rewrite eqEsubset; split=> [a [i ?]->| a [i ?]<-]; [apply imageP | exists i]. | |
| by rewrite eqEsubset; split=> [a [i ?]->| a [i ?]<-]; [apply: imageP | exists i]. |
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they are defined here https://github.com/affeldt-aist/infotheo/blob/master/lib/classical_sets_ext.v#L40-L53
and used in infotheo and monae, they may be of more general interest, at the very least this PR could help
us minimize dependencies from monae (see discussion affeldt-aist/monae#56)