Nuprl Lemma : decidable__fset-closed
∀[T:Type]. ∀eq:EqDecider(T). ∀fs:(T ⟶ T) List. ∀s:fset(T). Dec((s closed under fs))
Proof
Definitions occuring in Statement :
fset-closed: (s closed under fs),
fset: fset(T),
list: T List,
deq: EqDecider(T),
decidable: Dec(P),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
fset-closed: (s closed under fs),
member: t ∈ T,
so_lambda: λ2x.t[x],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q
Lemmas referenced :
decidable__l_all,
all_wf,
isect_wf,
fset-member_wf,
l_member_wf,
decidable__all_fset,
decidable__fset-member,
set_wf,
fset_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesisEquality,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
hypothesis,
applyEquality,
setElimination,
rename,
setEquality,
independent_functionElimination,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}eq:EqDecider(T). \mforall{}fs:(T {}\mrightarrow{} T) List. \mforall{}s:fset(T). Dec((s closed under fs))
Date html generated:
2016_05_14-PM-03_44_42
Last ObjectModification:
2015_12_26-PM-06_38_11
Theory : finite!sets
Home
Index