### Nuprl Lemma : bag-covers_wf

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

Proof

Definitions occuring in Statement :  bag-covers: `bag-covers(T;R;cvr;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-covers: `bag-covers(T;R;cvr;b)` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` infix_ap: `x f y` so_apply: `x[s]`
Lemmas referenced :  all_wf bag-member_wf or_wf exists_wf and_wf bag_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality lambdaEquality functionEquality hypothesis applyEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache cumulativity universeEquality

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

Date html generated: 2016_05_15-PM-03_12_23
Last ObjectModification: 2015_12_27-AM-09_23_29

Theory : bags

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