Nuprl Lemma : extd-nameset_subtype_int
∀[L:Cname List]. (extd-nameset(L) ⊆r ℤ)
Proof
Definitions occuring in Statement :
extd-nameset: extd-nameset(L),
coordinate_name: Cname,
list: T List,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
extd-nameset: extd-nameset(L),
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
nameset: nameset(L),
coordinate_name: Cname,
int_upper: {i...},
int_seg: {i..j-}
Lemmas referenced :
extd-nameset_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
unionElimination,
equalityElimination,
sqequalRule,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lemma_by_obid,
isectElimination,
axiomEquality
Latex:
\mforall{}[L:Cname List]. (extd-nameset(L) \msubseteq{}r \mBbbZ{})
Date html generated:
2016_05_20-AM-09_29_01
Last ObjectModification:
2015_12_28-PM-04_48_02
Theory : cubical!sets
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