Nuprl Lemma : list_all_wf
∀[T:Type]. ∀[l:T List]. ∀[P:T ⟶ ℙ]. (list_all(x.P[x];l) ∈ ℙ)
Proof
Definitions occuring in Statement :
list_all: list_all(x.P[x];l),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list_all: list_all(x.P[x];l),
prop: ℙ,
and: P ∧ Q,
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
reduce_wf,
istype-universe,
true_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
universeEquality,
lambdaEquality_alt,
productEquality,
applyEquality,
hypothesis,
because_Cache,
sqequalRule,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
isect_memberEquality_alt
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. (list\_all(x.P[x];l) \mmember{} \mBbbP{})
Date html generated:
2019_10_15-AM-10_53_57
Last ObjectModification:
2018_10_09-AM-10_28_15
Theory : list!
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