Nuprl Lemma : fset-contains-none_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[s:fset(T)]. ∀[Cs:T ⟶ fset(fset(T))]. (fset-contains-none(eq;s;x.Cs[x]) ∈ 𝔹)
Proof
Definitions occuring in Statement :
fset-contains-none: fset-contains-none(eq;s;x.Cs[x]),
fset: fset(T),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
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,
fset-contains-none: fset-contains-none(eq;s;x.Cs[x]),
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fset-contains-none-of_wf,
f-union_wf,
fset_wf,
deq-fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[s:fset(T)]. \mforall{}[Cs:T {}\mrightarrow{} fset(fset(T))].
(fset-contains-none(eq;s;x.Cs[x]) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-PM-03_42_18
Last ObjectModification:
2015_12_26-PM-06_39_41
Theory : finite!sets
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