Nuprl Lemma : lastn-0
∀[L:Top List]. ∀[n:ℤ]. lastn(n;L) ~ [] supposing n ≤ 0
Proof
Definitions occuring in Statement :
lastn: lastn(n;L),
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
le: A ≤ B,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
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,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
or: P ∨ Q,
cons: [a / b],
ge: i ≥ j ,
le: A ≤ B
Lemmas referenced :
lastn-cases,
le_wf,
list_wf,
top_wf,
le_int_wf,
length_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
lt_int_wf,
less_than_wf,
bnot_wf,
equal-wf-base,
int_subtype_base,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
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,
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
non_neg_length,
itermAdd_wf,
int_term_value_add_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalAxiom,
natural_numberEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality,
baseClosed,
baseApply,
closedConclusion,
applyEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
lambdaFormation,
unionElimination,
equalityElimination,
independent_functionElimination,
productElimination,
promote_hyp,
hypothesis_subsumption
Latex:
\mforall{}[L:Top List]. \mforall{}[n:\mBbbZ{}]. lastn(n;L) \msim{} [] supposing n \mleq{} 0
Date html generated:
2018_05_21-PM-06_31_50
Last ObjectModification:
2017_07_26-PM-04_51_19
Theory : general
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