Nuprl Lemma : nth_tl_decomp
∀[T:Type]. ∀[m:ℕ]. ∀[L:T List]. nth_tl(m;L) ~ [L[m] / nth_tl(1 + m;L)] supposing m < ||L||
Proof
Definitions occuring in Statement :
select: L[n],
length: ||as||,
nth_tl: nth_tl(n;as),
cons: [a / b],
list: T List,
nat: ℕ,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
nth_tl: nth_tl(n;as),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
subtract: n - m,
btrue: tt,
decidable: Dec(P),
or: P ∨ Q,
squash: ↓T,
less_than: a < b,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
sq_type: SQType(T),
assert: ↑b,
select: L[n],
nil: [],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
cons: [a / b]
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
length_wf,
list_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
nat_wf,
list_decomp,
select0,
tl_wf,
squash_wf,
true_wf,
length_tl,
subtype_rel_self,
iff_weakening_equal,
decidable__lt,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
non_neg_length,
itermAdd_wf,
int_term_value_add_lemma,
int_subtype_base,
list-cases,
reduce_tl_nil_lemma,
nth_tl_nil,
stuck-spread,
base_wf,
length_of_nil_lemma,
product_subtype_list,
reduce_tl_cons_lemma,
length_of_cons_lemma,
select-cons-tl
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
sqequalAxiom,
equalityTransitivity,
equalitySymmetry,
unionElimination,
because_Cache,
universeEquality,
applyEquality,
imageElimination,
productElimination,
imageMemberEquality,
baseClosed,
instantiate,
equalityElimination,
addEquality,
promote_hyp,
cumulativity,
hypothesis_subsumption
Latex:
\mforall{}[T:Type]. \mforall{}[m:\mBbbN{}]. \mforall{}[L:T List]. nth\_tl(m;L) \msim{} [L[m] / nth\_tl(1 + m;L)] supposing m < ||L||
Date html generated:
2018_05_21-PM-00_32_41
Last ObjectModification:
2018_05_19-AM-06_42_44
Theory : list_1
Home
Index