Nuprl Lemma : l_exists_wf
∀[T:Type]. ∀[L:T List]. ∀[P:{x:T| (x ∈ L)} ⟶ ℙ]. ((∃x∈L. P[x]) ∈ ℙ)
Proof
Definitions occuring in Statement :
l_exists: (∃x∈L. P[x]),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
l_exists: (∃x∈L. P[x]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uimplies: b supposing a,
int_seg: {i..j-},
sq_stable: SqStable(P),
implies: P ⇒ Q,
lelt: i ≤ j < k,
and: P ∧ Q,
squash: ↓T
Lemmas referenced :
list_wf,
sq_stable__le,
list-subtype,
l_member_wf,
select_wf,
length_wf,
int_seg_wf,
exists_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
setEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
setElimination,
rename,
independent_functionElimination,
productElimination,
imageMemberEquality,
baseClosed,
imageElimination,
axiomEquality,
functionEquality,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[P:\{x:T| (x \mmember{} L)\} {}\mrightarrow{} \mBbbP{}]. ((\mexists{}x\mmember{}L. P[x]) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-AM-06_39_36
Last ObjectModification:
2016_01_14-PM-08_21_14
Theory : list_0
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