Nuprl Lemma : uext_wf
∀[I,J:Cname List]. ∀[g:nameset(I) ⟶ extd-nameset(J)]. (uext(g) ∈ extd-nameset(I) ⟶ extd-nameset(J))
Proof
Definitions occuring in Statement :
uext: uext(g),
extd-nameset: extd-nameset(L),
nameset: nameset(L),
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uext: uext(g),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
subtype_rel: A ⊆r B
Lemmas referenced :
isname_wf,
bool_wf,
eqtt_to_assert,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
extd-nameset_wf,
nameset_wf,
list_wf,
coordinate_name_wf,
assert-isname,
not-assert-isname,
nsub2_subtype_extd-nameset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
cumulativity,
independent_functionElimination,
because_Cache,
voidElimination,
axiomEquality,
functionEquality,
isect_memberEquality,
applyEquality,
functionExtensionality
Latex:
\mforall{}[I,J:Cname List]. \mforall{}[g:nameset(I) {}\mrightarrow{} extd-nameset(J)].
(uext(g) \mmember{} extd-nameset(I) {}\mrightarrow{} extd-nameset(J))
Date html generated:
2017_10_05-AM-10_05_29
Last ObjectModification:
2017_07_28-AM-11_16_04
Theory : cubical!sets
Home
Index