Nuprl Lemma : ml-filter_wf
∀[A:Type]. ∀[P:A ⟶ 𝔹]. ∀[l:A List]. (ml-filter(P;l) ∈ A List) supposing valueall-type(A) ∧ A
Proof
Definitions occuring in Statement :
ml-filter: ml-filter(P;L),
list: T List,
valueall-type: valueall-type(T),
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
and: P ∧ Q,
cand: A c∧ B,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
ml-filter-sq,
filter_wf5,
subtype_rel_dep_function,
bool_wf,
l_member_wf,
subtype_rel_self,
set_wf,
list_wf,
valueall-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
extract_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
independent_pairFormation,
cumulativity,
applyEquality,
because_Cache,
lambdaEquality,
setEquality,
setElimination,
rename,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
functionEquality,
productEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. \mforall{}[l:A List]. (ml-filter(P;l) \mmember{} A List) supposing valueall-type(A) \mwedge{} A
Date html generated:
2017_09_29-PM-05_50_59
Last ObjectModification:
2017_05_19-PM-02_20_15
Theory : ML
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