Nuprl Lemma : lapp_fact_b
∀T:Type. ∀as:T List.  (as = (Π 0 ≤ i < ||as||. [as[i]]) ∈ (T List))
Proof
Definitions occuring in Statement : 
lapp_imon: <T List,@>
, 
select: L[n]
, 
length: ||as||
, 
cons: [a / b]
, 
nil: []
, 
list: T List
, 
all: ∀x:A. B[x]
, 
natural_number: $n
, 
universe: Type
, 
equal: s = t ∈ T
, 
mon_itop: Π lb ≤ i < ub. E[i]
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
squash: ↓T
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
, 
grp_car: |g|
, 
pi1: fst(t)
, 
lapp_imon: <T List,@>
, 
list: T List
, 
true: True
, 
uimplies: b supposing a
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
Lemmas referenced : 
list_wf, 
lapp_fact_a, 
equal_wf, 
squash_wf, 
true_wf, 
istype-universe, 
mon_for_eq_itop, 
lapp_imon_wf, 
cons_wf, 
nil_wf, 
subtype_rel_self, 
iff_weakening_equal
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation_alt, 
cut, 
hypothesis, 
universeIsType, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
universeEquality, 
dependent_functionElimination, 
applyEquality, 
lambdaEquality_alt, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
inhabitedIsType, 
because_Cache, 
sqequalRule, 
natural_numberEquality, 
imageMemberEquality, 
baseClosed, 
instantiate, 
independent_isectElimination, 
productElimination, 
independent_functionElimination
Latex:
\mforall{}T:Type.  \mforall{}as:T  List.    (as  =  (\mPi{}  0  \mleq{}  i  <  ||as||.  [as[i]]))
Date html generated:
2019_10_16-PM-01_03_11
Last ObjectModification:
2018_10_08-AM-11_41_08
Theory : list_2
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