Nuprl Lemma : isname_wf
∀[L:Cname List]. ∀[z:extd-nameset(L)]. (isname(z) ∈ 𝔹)
Proof
Definitions occuring in Statement :
isname: isname(z),
extd-nameset: extd-nameset(L),
coordinate_name: Cname,
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
isname: isname(z),
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 :
le_int_wf,
extd-nameset_wf,
list_wf,
coordinate_name_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
imageElimination,
productElimination,
thin,
unionElimination,
equalityElimination,
sqequalRule,
lemma_by_obid,
isectElimination,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[L:Cname List]. \mforall{}[z:extd-nameset(L)]. (isname(z) \mmember{} \mBbbB{})
Date html generated:
2016_05_20-AM-09_29_12
Last ObjectModification:
2015_12_28-PM-04_47_44
Theory : cubical!sets
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