Nuprl Lemma : lastn-cases
∀[L:Top List]. ∀[n:ℤ]. (lastn(n;L) ~ if ||L|| ≤z n then L if n ≤z 0 then [] else lastn(n;tl(L)) fi )
Proof
Definitions occuring in Statement :
lastn: lastn(n;L),
length: ||as||,
tl: tl(l),
nil: [],
list: T List,
le_int: i ≤z j,
ifthenelse: if b then t else f fi ,
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
lastn: lastn(n;L),
nth_tl: nth_tl(n;as),
le: A ≤ B,
and: P ∧ Q,
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,
prop: ℙ,
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
guard: {T},
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
cons: [a / b],
sq_type: SQType(T)
Lemmas referenced :
list_wf,
top_wf,
le_int_wf,
length_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
le_wf,
subtract_wf,
lt_int_wf,
less_than_wf,
bnot_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
equal-wf-base,
int_subtype_base,
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,
nth_tl_is_nil,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
tl_wf,
list-cases,
length_of_nil_lemma,
reduce_tl_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
reduce_tl_cons_lemma,
add-is-int-iff,
itermAdd_wf,
int_term_value_add_lemma,
false_wf,
subtype_base_sq,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
intEquality,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
extract_by_obid,
equalityTransitivity,
equalitySymmetry,
baseClosed,
natural_numberEquality,
productElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
baseApply,
closedConclusion,
applyEquality,
lambdaFormation,
unionElimination,
equalityElimination,
independent_functionElimination,
dependent_set_memberEquality,
promote_hyp,
hypothesis_subsumption,
addEquality,
pointwiseFunctionality,
rename,
instantiate,
cumulativity
Latex:
\mforall{}[L:Top List]. \mforall{}[n:\mBbbZ{}].
(lastn(n;L) \msim{} if ||L|| \mleq{}z n then L
if n \mleq{}z 0 then []
else lastn(n;tl(L))
fi )
Date html generated:
2018_05_21-PM-06_31_00
Last ObjectModification:
2017_07_26-PM-04_51_02
Theory : general
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