Nuprl Lemma : p-filter_wf
∀[T:Type]. ∀[P:T ⟶ ℙ]. ∀[f:∀x:T. Dec(P[x])]. (p-filter(f) ∈ T ⟶ (T + Top))
Proof
Definitions occuring in Statement :
p-filter: p-filter(f),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
p-filter: p-filter(f),
decidable: Dec(P),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_apply: x[s],
implies: P ⇒ Q,
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
or_wf,
not_wf,
subtype_rel_self,
top_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
applyEquality,
hypothesisEquality,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
lambdaFormation,
equalityTransitivity,
equalitySymmetry,
unionEquality,
instantiate,
universeEquality,
unionElimination,
inlEquality,
inrEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
functionEquality,
because_Cache,
cumulativity
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. \mforall{}[f:\mforall{}x:T. Dec(P[x])]. (p-filter(f) \mmember{} T {}\mrightarrow{} (T + Top))
Date html generated:
2019_10_15-AM-11_07_30
Last ObjectModification:
2018_08_21-PM-01_59_01
Theory : general
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