Nuprl Lemma : dset_list_wf
∀s:DSet. (s List ∈ DSet)
Proof
Definitions occuring in Statement :
dset_list: s List,
all: ∀x:A. B[x],
member: t ∈ T,
dset: DSet
Definitions unfolded in proof :
dset_list: s List,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
dset: DSet,
uimplies: b supposing a,
eqfun_p: IsEqFun(T;eq),
infix_ap: x f y,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
mk_dset_wf,
list_wf,
set_car_wf,
eq_list_wf,
assert_wf,
assert_witness,
equal_wf,
dset_wf,
assert_of_eq_list
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
dependent_functionElimination,
because_Cache,
independent_isectElimination,
isect_memberFormation,
introduction,
independent_pairFormation,
independent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}s:DSet. (s List \mmember{} DSet)
Date html generated:
2016_05_16-AM-07_34_56
Last ObjectModification:
2015_12_28-PM-05_46_17
Theory : list_2
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