Nuprl Lemma : fset-names-to-list
∀[I:fset(ℕ)]. ∀s:fset(names(I)). ∃L:names(I) List. (L = s ∈ fset(names(I)))
Proof
Definitions occuring in Statement :
names: names(I),
fset: fset(T),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
names: names(I),
nat: ℕ,
implies: P ⇒ Q,
linorder: Linorder(T;x,y.R[x; y]),
and: P ∧ Q,
order: Order(T;x,y.R[x; y]),
refl: Refl(T;x,y.E[x; y]),
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
cand: A c∧ B,
trans: Trans(T;x,y.E[x; y]),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_stable: SqStable(P),
squash: ↓T,
le: A ≤ B,
anti_sym: AntiSym(T;x,y.R[x; y]),
connex: Connex(T;x,y.R[x; y]),
fset: fset(T),
quotient: x,y:A//B[x; y],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
fset-member: a ∈ s,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
set-equal: set-equal(T;x;y),
equiv_rel: EquivRel(T;x,y.E[x; y]),
guard: {T},
sym: Sym(T;x,y.E[x; y])
Lemmas referenced :
fset-to-list,
names_wf,
names-deq_wf,
le_wf,
decidable__le,
fset_wf,
nat_wf,
nat_properties,
satisfiable-full-omega-tt,
intformnot_wf,
intformle_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
sq_stable_from_decidable,
fset-member_wf,
int-deq_wf,
strong-subtype-deq-subtype,
strong-subtype-set3,
strong-subtype-self,
decidable__fset-member,
intformand_wf,
int_formula_prop_and_lemma,
less_than'_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
itermConstant_wf,
int_term_value_constant_lemma,
decidable__or,
intformor_wf,
int_formula_prop_or_lemma,
equal_wf,
list_subtype_fset,
quotient-member-eq,
list_wf,
set-equal_wf,
set-equal-equiv,
equal-wf-base,
assert-deq-member,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
lambdaEquality,
setElimination,
rename,
independent_functionElimination,
sqequalRule,
because_Cache,
independent_pairFormation,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
applyEquality,
imageMemberEquality,
baseClosed,
imageElimination,
productElimination,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
pointwiseFunctionalityForEquality,
pertypeElimination,
productEquality,
allFunctionality,
promote_hyp
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}s:fset(names(I)). \mexists{}L:names(I) List. (L = s)
Date html generated:
2017_02_21-AM-10_30_49
Last ObjectModification:
2017_02_02-PM-06_35_41
Theory : cubical!type!theory
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