Nuprl Lemma : list-closed_wf
∀[T:Type]. ∀[L:T List]. ∀[f:T ⟶ (T List)]. (list-closed(T;L;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
list-closed: list-closed(T;L;f),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list-closed: list-closed(T;L;f),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
l_all_wf,
l_member_wf,
list_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
Error :lambdaEquality_alt,
applyEquality,
setElimination,
rename,
hypothesis,
Error :setIsType,
Error :universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsType,
Error :inhabitedIsType,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[f:T {}\mrightarrow{} (T List)]. (list-closed(T;L;f) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-01_50_47
Last ObjectModification:
2019_05_13-PM-03_36_23
Theory : list_1
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