### Nuprl Lemma : bag-cover_wf

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[cvr,b:bag(T)].  (bag-cover(T;R;cvr;b) ∈ ℙ)`

Proof

Definitions occuring in Statement :  bag-cover: `bag-cover(T;R;mx;b)` bag: `bag(T)` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` bag-cover: `bag-cover(T;R;mx;b)` prop: `ℙ`
Lemmas referenced :  and_wf sub-bag_wf bag-covers_wf bag-incomparable_wf bag_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache functionEquality cumulativity universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[cvr,b:bag(T)].    (bag-cover(T;R;cvr;b)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-03_12_33
Last ObjectModification: 2015_12_27-AM-09_23_23

Theory : bags

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