Nuprl Lemma : fset-contains-none-of_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[s:fset(T)]. ∀[cs:fset(fset(T))]. (fset-contains-none-of(eq;s;cs) ∈ 𝔹)
Proof
Definitions occuring in Statement :
fset-contains-none-of: fset-contains-none-of(eq;s;cs),
fset: fset(T),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset-contains-none-of: fset-contains-none-of(eq;s;cs),
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
fset-null_wf,
fset_wf,
fset-filter_wf,
deq-f-subset_wf,
bool_wf,
all_wf,
iff_wf,
f-subset_wf,
assert_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,
setElimination,
rename,
setEquality,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[s:fset(T)]. \mforall{}[cs:fset(fset(T))].
(fset-contains-none-of(eq;s;cs) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-PM-03_42_05
Last ObjectModification:
2015_12_26-PM-06_39_57
Theory : finite!sets
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