Nuprl Lemma : atom_dset_wf
atom_dset() ∈ DSet
Proof
Definitions occuring in Statement :
atom_dset: atom_dset(),
dset: DSet,
member: t ∈ T
Definitions unfolded in proof :
atom_dset: atom_dset(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
eqfun_p: IsEqFun(T;eq),
infix_ap: x f y,
uiff: uiff(P;Q),
and: P ∧ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
mk_dset_wf,
eq_atom_wf,
equal-wf-base,
atom_subtype_base,
iff_weakening_uiff,
assert_wf,
assert_of_eq_atom,
assert_witness,
uall_wf,
uiff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
atomEquality,
lambdaEquality,
hypothesisEquality,
hypothesis,
because_Cache,
independent_isectElimination,
sqequalRule,
isect_memberFormation,
independent_pairFormation,
applyEquality,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
addLevel,
uallFunctionality,
independent_functionElimination,
cumulativity,
instantiate
Latex:
atom\_dset() \mmember{} DSet
Date html generated:
2017_10_01-AM-08_13_25
Last ObjectModification:
2017_02_28-PM-01_57_36
Theory : sets_1
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