Nuprl Lemma : tl_nth_tl
∀[n:ℕ]. ∀[L:Top List]. (tl(nth_tl(n;L)) ~ nth_tl(n;tl(L)))
Proof
Definitions occuring in Statement :
nth_tl: nth_tl(n;as),
tl: tl(l),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
top: Top,
all: ∀x:A. B[x],
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 ,
btrue: tt,
subtract: n - m,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
uimplies: b supposing a,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
decidable: Dec(P)
Lemmas referenced :
nth_tl_nth_tl,
false_wf,
le_wf,
list_wf,
top_wf,
nat_wf,
equal_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermAdd_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
set_subtype_base,
int_subtype_base,
decidable__equal_int,
subtract_wf,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
decidable__le
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
hypothesisEquality,
sqequalAxiom,
isect_memberEquality,
because_Cache,
voidElimination,
voidEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
addEquality,
setElimination,
rename,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
promote_hyp,
instantiate,
cumulativity
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[L:Top List]. (tl(nth\_tl(n;L)) \msim{} nth\_tl(n;tl(L)))
Date html generated:
2017_04_14-AM-09_26_12
Last ObjectModification:
2017_02_27-PM-04_00_10
Theory : list_1
Home
Index