Nuprl Lemma : fset-null_wf
∀[T:Type]. ∀[s:fset(T)]. (fset-null(s) ∈ 𝔹)
Proof
Definitions occuring in Statement :
fset-null: fset-null(s),
fset: fset(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: fset(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
fset-null: fset-null(s),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
cons: [a / b],
top: Top,
set-equal: set-equal(T;x;y),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
not: ¬A,
false: False
Lemmas referenced :
bool_wf,
equal-wf-base,
list_wf,
set-equal_wf,
fset_wf,
equal_wf,
list-cases,
null_nil_lemma,
btrue_wf,
product_subtype_list,
null_cons_lemma,
cons_member,
l_member_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
extract_by_obid,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
thin,
productEquality,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
unionElimination,
promote_hyp,
hypothesis_subsumption,
rename,
voidElimination,
voidEquality,
inlFormation,
independent_isectElimination
Latex:
\mforall{}[T:Type]. \mforall{}[s:fset(T)]. (fset-null(s) \mmember{} \mBbbB{})
Date html generated:
2017_04_17-AM-09_19_53
Last ObjectModification:
2017_02_27-PM-05_23_26
Theory : finite!sets
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