Nuprl Lemma : fset-closure_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[fs:(T ⟶ T) List]. ∀[s,c:fset(T)]. ((c = fs closure of s) ∈ ℙ)
Proof
Definitions occuring in Statement :
fset-closure: (c = fs closure of s),
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-closure: (c = fs closure of s),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
Lemmas referenced :
and_wf,
f-subset_wf,
fset-closed_wf,
all_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,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[fs:(T {}\mrightarrow{} T) List]. \mforall{}[s,c:fset(T)]. ((c = fs closure of s) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_44_52
Last ObjectModification:
2015_12_26-PM-06_38_03
Theory : finite!sets
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