Nuprl Lemma : l_interval_wf
∀[T:Type]. ∀[l:T List]. ∀[i:ℕ||l||]. ∀[j:ℕi + 1].  (l_interval(l;j;i) ∈ T List)
Proof
Definitions occuring in Statement : 
l_interval: l_interval(l;j;i)
, 
length: ||as||
, 
list: T List
, 
int_seg: {i..j-}
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
add: n + m
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
l_interval: l_interval(l;j;i)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
nat: ℕ
, 
int_seg: {i..j-}
, 
guard: {T}
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
top: Top
, 
prop: ℙ
, 
less_than: a < b
, 
squash: ↓T
Lemmas referenced : 
list_wf, 
int_seg_wf, 
decidable__lt, 
select_wf, 
le_wf, 
int_formula_prop_wf, 
int_term_value_add_lemma, 
int_formula_prop_less_lemma, 
int_term_value_var_lemma, 
int_term_value_subtract_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_le_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_and_lemma, 
itermAdd_wf, 
intformless_wf, 
itermVar_wf, 
itermSubtract_wf, 
itermConstant_wf, 
intformle_wf, 
intformnot_wf, 
intformand_wf, 
satisfiable-full-omega-tt, 
decidable__le, 
length_wf, 
int_seg_properties, 
subtract_wf, 
mklist_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
dependent_set_memberEquality, 
setElimination, 
rename, 
hypothesis, 
natural_numberEquality, 
addEquality, 
productElimination, 
dependent_functionElimination, 
unionElimination, 
independent_isectElimination, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
independent_pairFormation, 
computeAll, 
because_Cache, 
imageElimination, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[l:T  List].  \mforall{}[i:\mBbbN{}||l||].  \mforall{}[j:\mBbbN{}i  +  1].    (l\_interval(l;j;i)  \mmember{}  T  List)
Date html generated:
2016_05_14-PM-01_45_56
Last ObjectModification:
2016_01_15-AM-08_21_07
Theory : list_1
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