Nuprl Lemma : isname-nameset
∀[L:Cname List]. ∀[z:nameset(L)]. (isname(z) ~ tt)
Proof
Definitions occuring in Statement :
isname: isname(z),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
btrue: tt,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nameset: nameset(L),
coordinate_name: Cname,
int_upper: {i...},
isname: isname(z),
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
true: True,
prop: ℙ,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T}
Lemmas referenced :
subtype_base_sq,
bool_subtype_base,
iff_imp_equal_bool,
le_int_wf,
btrue_wf,
le_wf,
true_wf,
assert_of_le_int,
assert_wf,
iff_wf,
nameset_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
sqequalHypSubstitution,
setElimination,
thin,
rename,
cut,
sqequalAxiom,
instantiate,
lemma_by_obid,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
natural_numberEquality,
hypothesisEquality,
independent_pairFormation,
lambdaFormation,
addLevel,
productElimination,
impliesFunctionality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}[L:Cname List]. \mforall{}[z:nameset(L)]. (isname(z) \msim{} tt)
Date html generated:
2016_05_20-AM-09_29_14
Last ObjectModification:
2015_12_28-PM-04_47_46
Theory : cubical!sets
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