Nuprl Lemma : empty-fset-contains-none
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[Cs:T ⟶ fset(fset(T))]. (↑fset-contains-none(eq;{};x.Cs[x]))
Proof
Definitions occuring in Statement :
fset-contains-none: fset-contains-none(eq;s;x.Cs[x]),
empty-fset: {},
fset: fset(T),
deq: EqDecider(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
fset-member: a ∈ s,
assert: ↑b,
ifthenelse: if b then t else f fi ,
deq-member: x ∈b L,
reduce: reduce(f;k;as),
list_ind: list_ind,
empty-fset: {},
nil: [],
it: ⋅,
bfalse: ff,
prop: ℙ
Lemmas referenced :
assert-fset-contains-none,
empty-fset_wf,
f-subset_wf,
fset-member_wf,
fset_wf,
deq-fset_wf,
fset-contains-none_wf,
deq_wf,
assert_witness
Rules used in proof :
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
applyEquality,
productElimination,
independent_isectElimination,
lambdaFormation,
independent_functionElimination,
voidElimination,
because_Cache,
functionEquality,
universeEquality,
isect_memberFormation,
introduction,
isect_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[Cs:T {}\mrightarrow{} fset(fset(T))]. (\muparrow{}fset-contains-none(eq;\{\};x.Cs[x]))
Date html generated:
2016_05_14-PM-03_42_24
Last ObjectModification:
2015_12_26-PM-06_39_39
Theory : finite!sets
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