Nuprl Lemma : fset-closed_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[fs:(T ⟶ T) List]. ∀[s:fset(T)]. ((s closed under fs) ∈ ℙ)
Proof
Definitions occuring in Statement :
fset-closed: (s closed under fs),
fset: fset(T),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fset-closed: (s closed under fs),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
l_all_wf,
all_wf,
isect_wf,
fset-member_wf,
l_member_wf,
fset_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
applyEquality,
setElimination,
rename,
setEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[fs:(T {}\mrightarrow{} T) List]. \mforall{}[s:fset(T)]. ((s closed under fs) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_44_39
Last ObjectModification:
2015_12_26-PM-06_38_17
Theory : finite!sets
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