Nuprl Lemma : select-nth_tl
∀[n,x:ℕ]. ∀[L:Top List]. (nth_tl(n;L)[x] ~ L[n + x])
Proof
Definitions occuring in Statement :
select: L[n],
nth_tl: nth_tl(n;as),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
add: n + m,
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,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
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,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {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,
satisfiable-full-omega-tt,
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,
list_wf,
top_wf,
nat_wf,
zero-add,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
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,
tl_wf,
list-cases,
reduce_tl_nil_lemma,
stuck-spread,
base_wf,
product_subtype_list,
reduce_tl_cons_lemma,
select-cons-tl,
decidable__lt,
itermAdd_wf,
int_term_value_add_lemma,
general_arith_equation1
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,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
independent_functionElimination,
sqequalAxiom,
because_Cache,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
promote_hyp,
instantiate,
cumulativity,
baseClosed,
hypothesis_subsumption,
addEquality
Latex:
\mforall{}[n,x:\mBbbN{}]. \mforall{}[L:Top List]. (nth\_tl(n;L)[x] \msim{} L[n + x])
Date html generated:
2017_04_17-AM-07_49_32
Last ObjectModification:
2017_02_27-PM-04_23_49
Theory : list_1
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