Nuprl Lemma : dset_set_wf
∀[s:DSet]. ∀[Q:|s| ⟶ ℙ]. ({x:s| Q[x]} ∈ DSet)
Proof
Definitions occuring in Statement :
dset_set: dset_set,
dset: DSet,
set_car: |p|,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
dset_set: dset_set,
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
prop: ℙ,
uimplies: b supposing a,
all: ∀x:A. B[x],
eqfun_p: IsEqFun(T;eq),
uiff: uiff(P;Q),
and: P ∧ Q,
infix_ap: x f y,
implies: P ⇒ Q
Lemmas referenced :
mk_dset_wf,
set_car_wf,
set_eq_wf,
subtype_rel_dep_function,
bool_wf,
subtype_rel_self,
set_wf,
dset_wf,
eqfun_p_subtyping,
assert_wf,
assert_witness,
equal_wf,
assert_of_dset_eq
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
applyEquality,
because_Cache,
lambdaEquality,
functionEquality,
universeEquality,
independent_isectElimination,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
isect_memberEquality,
productElimination,
independent_pairEquality,
independent_functionElimination
Latex:
\mforall{}[s:DSet]. \mforall{}[Q:|s| {}\mrightarrow{} \mBbbP{}]. (\{x:s| Q[x]\} \mmember{} DSet)
Date html generated:
2016_05_15-PM-00_05_56
Last ObjectModification:
2015_12_26-PM-11_27_42
Theory : sets_1
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