Nuprl Lemma : isaxiom-wf-colist
∀[T:Type]. ∀[x:colist(T)]. (isaxiom(x) ∈ 𝔹)
Proof
Definitions occuring in Statement :
colist: colist(T),
bfalse: ff,
btrue: tt,
bool: 𝔹,
uall: ∀[x:A]. B[x],
isaxiom: if z = Ax then a otherwise b,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t)
Lemmas referenced :
colist-ext,
colist_wf,
btrue_wf,
bfalse_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
productElimination,
introduction,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
hypothesis_subsumption,
applyEquality,
imageElimination,
unionElimination,
equalityElimination
Latex:
\mforall{}[T:Type]. \mforall{}[x:colist(T)]. (isaxiom(x) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-AM-06_25_25
Last ObjectModification:
2015_12_26-PM-00_42_30
Theory : list_0
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