Nuprl Lemma : test-afoo_wf
∀[x:Atom]. (test-afoo(x) ∈ test-foo())
Proof
Definitions occuring in Statement :
test-afoo: test-afoo(x),
test-foo: test-foo(),
uall: ∀[x:A]. B[x],
member: t ∈ T,
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
test-foo: test-foo(),
test-afoo: test-afoo(x),
member: t ∈ T,
subtype_rel: A ⊆r B,
tuple-type: tuple-type(L),
list_ind: list_ind,
prec-arg-types: prec-arg-types(lbl,p.a[lbl; p];i;lbl),
map: map(f;as),
mrec-spec: mrec-spec(L;lbl;p),
apply-alist: apply-alist(eq;L;x),
test-Spec: test-Spec(),
cons: [a / b],
ifthenelse: if b then t else f fi ,
atom-deq: AtomDeq,
eq_atom: x =a y,
pi1: fst(t),
bfalse: ff,
btrue: tt,
pi2: snd(t),
null: null(as),
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
length: ||as||,
true: True,
and: P ∧ Q
Lemmas referenced :
mk-prec_wf-mrec,
test-Spec_wf,
subtype_rel_self,
tuple-type_wf,
prec-arg-types_wf,
mrec-spec_wf,
istype-atom
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
closedConclusion,
tokenEquality,
hypothesisEquality,
applyEquality,
atomEquality,
lambdaEquality_alt,
inhabitedIsType,
independent_isectElimination,
independent_pairFormation,
natural_numberEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[x:Atom]. (test-afoo(x) \mmember{} test-foo())
Date html generated:
2019_10_15-AM-10_48_41
Last ObjectModification:
2019_03_25-PM-01_47_51
Theory : tree_1
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