Nuprl Lemma : last_l_interval
∀[T:Type]. ∀[l:T List]. ∀[i:ℕ||l||]. ∀[j:ℕi]. (last(l_interval(l;j;i)) = l[i - 1] ∈ T)
Proof
Definitions occuring in Statement :
l_interval: l_interval(l;j;i),
last: last(L),
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
subtract: n - m,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
last: last(L),
squash: ↓T,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
guard: {T},
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,
le: A ≤ B,
less_than: a < b,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T),
subtract: n - m
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
select_l_interval,
int_seg_properties,
length_wf,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
lelt_wf,
subtract_wf,
l_interval_wf,
le_wf,
length_l_interval,
iff_weakening_equal,
decidable__le,
intformle_wf,
itermSubtract_wf,
int_formula_prop_le_lemma,
int_term_value_subtract_lemma,
less_than_wf,
select_wf,
subtype_base_sq,
int_subtype_base,
int_seg_wf,
list_wf,
add-associates,
minus-one-mul,
add-swap,
add-mul-special,
add-commutes,
zero-mul,
add-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
setElimination,
rename,
dependent_set_memberEquality,
productElimination,
independent_pairFormation,
natural_numberEquality,
cumulativity,
dependent_functionElimination,
addEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
imageMemberEquality,
baseClosed,
independent_functionElimination,
universeEquality,
instantiate,
axiomEquality,
multiplyEquality,
minusEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[i:\mBbbN{}||l||]. \mforall{}[j:\mBbbN{}i]. (last(l\_interval(l;j;i)) = l[i - 1])
Date html generated:
2017_04_17-AM-07_42_56
Last ObjectModification:
2017_02_27-PM-04_15_21
Theory : list_1
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