### Nuprl Lemma : b_all_wf

`∀[T:Type]. ∀[b:bag(T)]. ∀[P:T ⟶ ℙ].  (b_all(T;b;x.P[x]) ∈ ℙ)`

Proof

Definitions occuring in Statement :  b_all: `b_all(T;b;x.P[x])` bag: `bag(T)` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` b_all: `b_all(T;b;x.P[x])` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` so_apply: `x[s]`
Lemmas referenced :  all_wf bag-member_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 cumulativity universeEquality isect_memberEquality because_Cache

Latex:
\mforall{}[T:Type].  \mforall{}[b:bag(T)].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbP{}].    (b\_all(T;b;x.P[x])  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-02_41_10
Last ObjectModification: 2015_12_27-AM-09_40_55

Theory : bags

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