Nuprl Lemma : names-list_wf
∀[I:fset(ℕ)]. ∀[s:fset(names(I))]. (names-list(s) ∈ {L:names(I) List| L = s ∈ fset(names(I))} )
Proof
Definitions occuring in Statement :
names-list: names-list(s),
names: names(I),
fset: fset(T),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
names-list: names-list(s),
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
uimplies: b supposing a,
so_apply: x[s],
exists: ∃x:A. B[x],
prop: ℙ,
implies: P ⇒ Q,
pi1: fst(t)
Lemmas referenced :
fset-names-to-list,
fset_wf,
nat_wf,
names_wf,
exists_wf,
list_wf,
equal_wf,
list_subtype_fset
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
thin,
instantiate,
extract_by_obid,
hypothesis,
lambdaEquality,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
sqequalHypSubstitution,
functionEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
productElimination,
dependent_set_memberEquality,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[s:fset(names(I))]. (names-list(s) \mmember{} \{L:names(I) List| L = s\} )
Date html generated:
2017_10_05-AM-00_59_14
Last ObjectModification:
2017_03_02-PM-10_18_12
Theory : cubical!type!theory
Home
Index