### Nuprl Lemma : bl-rev-exists_wf

`∀[T:Type]. ∀[L:T List]. ∀[P:{x:T| (x ∈ L)}  ⟶ 𝔹].  ((∃x∈rev(L).P[x])_b ∈ 𝔹)`

Proof

Definitions occuring in Statement :  bl-rev-exists: `(∃x∈rev(L).P[x])_b` l_member: `(x ∈ l)` list: `T List` bool: `𝔹` uall: `∀[x:A]. B[x]` so_apply: `x[s]` member: `t ∈ T` set: `{x:A| B[x]} ` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` prop: `ℙ` so_lambda: `λ2x.t[x]` so_apply: `x[s]`
Lemmas referenced :  bl-rev-exists-sq l_member_wf bool_wf list_wf bl-exists_wf
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation hypothesis sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule functionEquality setEquality universeEquality lambdaEquality applyEquality

Latex:
\mforall{}[T:Type].  \mforall{}[L:T  List].  \mforall{}[P:\{x:T|  (x  \mmember{}  L)\}    {}\mrightarrow{}  \mBbbB{}].    ((\mexists{}x\mmember{}rev(L).P[x])\_b  \mmember{}  \mBbbB{})

Date html generated: 2016_05_15-PM-03_49_02
Last ObjectModification: 2015_12_27-PM-01_22_14

Theory : general

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