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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