Nuprl Lemma : length_l_interval
∀[T:Type]. ∀[l:T List]. ∀[i:ℕ||l||]. ∀[j:ℕi + 1]. (||l_interval(l;j;i)|| = (i - j) ∈ ℤ)
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],
subtract: n - m,
add: n + m,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
l_interval: l_interval(l;j;i),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
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,
prop: ℙ
Lemmas referenced :
list_wf,
int_seg_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_length
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_set_memberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
addEquality,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
because_Cache,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[i:\mBbbN{}||l||]. \mforall{}[j:\mBbbN{}i + 1]. (||l\_interval(l;j;i)|| = (i - j))
Date html generated:
2016_05_14-PM-01_46_02
Last ObjectModification:
2016_01_15-AM-08_20_35
Theory : list_1
Home
Index