Nuprl Lemma : nth_tl_nil
∀[n:ℤ]. (nth_tl(n;[]) ~ [])
Proof
Definitions occuring in Statement :
nth_tl: nth_tl(n;as),
nil: [],
uall: ∀[x:A]. B[x],
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
btrue: tt,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
guard: {T}
Lemmas referenced :
le_int_wf,
bool_wf,
equal-wf-base,
int_subtype_base,
assert_wf,
le_wf,
lt_int_wf,
less_than_wf,
bnot_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
reduce_tl_nil_lemma,
uiff_transitivity,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
intWeakElimination,
sqequalHypSubstitution,
thin,
rename,
hypothesis,
sqequalRule,
sqequalAxiom,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
intEquality,
extract_by_obid,
isectElimination,
hypothesisEquality,
natural_numberEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
lambdaFormation,
unionElimination,
equalityElimination,
independent_functionElimination,
productElimination
Latex:
\mforall{}[n:\mBbbZ{}]. (nth\_tl(n;[]) \msim{} [])
Date html generated:
2017_04_14-AM-09_25_07
Last ObjectModification:
2017_02_27-PM-03_59_30
Theory : list_1
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