Nuprl Lemma : test-diamond_wf
∀[x1:test-foo()]. ∀[x:test-prop()]. (test-diamond(x1;x) ∈ test-prop())
Proof
Definitions occuring in Statement :
test-diamond: test-diamond(x1;x)
,
test-prop: test-prop()
,
test-foo: test-foo()
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
test-prop: test-prop()
,
test-diamond: test-diamond(x1;x)
,
member: t ∈ T
,
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)
,
prec: prec(lbl,p.a[lbl; p];i)
,
test-foo: test-foo()
,
mrec: mrec(L;i)
,
nil: []
,
it: ⋅
,
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,
test-prop_wf,
test-foo_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
closedConclusion,
tokenEquality,
independent_pairEquality,
hypothesisEquality,
independent_isectElimination,
independent_pairFormation,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeIsType
Latex:
\mforall{}[x1:test-foo()]. \mforall{}[x:test-prop()]. (test-diamond(x1;x) \mmember{} test-prop())
Date html generated:
2019_10_15-AM-10_49_11
Last ObjectModification:
2019_03_25-PM-01_48_14
Theory : tree_1
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