Nuprl Lemma : nil_wf
∀[T:Type]. ([] ∈ T List)
Proof
Definitions occuring in Statement :
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
list: T List,
uimplies: b supposing a,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
nil: [],
ext-eq: A ≡ B,
and: P ∧ Q,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
ifthenelse: if b then t else f fi ,
btrue: tt,
pi2: snd(t),
subtype_rel: A ⊆r B,
colength: colength(L),
has-value: (a)↓,
it: ⋅
Lemmas referenced :
is-exception_wf,
has-value_wf_base,
colist_wf,
unit_wf2,
ifthenelse_wf,
it_wf,
btrue_wf,
colist-ext,
colength_wf,
int-value-type,
le_wf,
set-value-type,
nat_wf,
has-value_wf-partial
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
dependent_set_memberEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
independent_isectElimination,
sqequalRule,
intEquality,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
productElimination,
imageMemberEquality,
dependent_pairEquality,
instantiate,
productEquality,
baseClosed,
applyEquality,
divergentSqle,
sqleReflexivity
Latex:
\mforall{}[T:Type]. ([] \mmember{} T List)
Date html generated:
2016_05_14-AM-06_25_44
Last ObjectModification:
2016_01_14-PM-08_26_47
Theory : list_0
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