Nuprl Lemma : last-map
∀[as:Top List]. ∀[f:Top]. last(map(f;as)) ~ f last(as) supposing ¬↑null(as)
Proof
Definitions occuring in Statement :
last: last(L),
null: null(as),
map: map(f;as),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
not: ¬A,
apply: f a,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
last: last(L),
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
not: ¬A,
implies: P ⇒ Q,
true: True,
false: False,
cons: [a / b],
top: Top,
bfalse: ff,
guard: {T},
nat: ℕ,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
sq_stable: SqStable(P),
squash: ↓T,
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
prop: ℙ
Lemmas referenced :
length-map,
top_wf,
select-map,
subtract_nat_wf,
length_wf,
list-cases,
length_of_nil_lemma,
null_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
istype-void,
null_cons_lemma,
length_wf_nat,
decidable__le,
istype-false,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-add,
istype-int,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-associates,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel2,
nat_properties,
subtract-is-int-iff,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
itermSubtract_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
false_wf,
decidable__lt,
subtract_wf,
intformless_wf,
int_formula_prop_less_lemma,
le_wf,
less_than_wf,
not_wf,
assert_wf,
null_wf,
istype-top,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
Error :dependent_set_memberEquality_alt,
independent_pairFormation,
natural_numberEquality,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
independent_functionElimination,
voidElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
Error :isect_memberEquality_alt,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
setElimination,
rename,
addEquality,
imageMemberEquality,
baseClosed,
imageElimination,
applyEquality,
Error :lambdaEquality_alt,
minusEquality,
Error :equalityIsType1,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
pointwiseFunctionality,
baseApply,
closedConclusion,
approximateComputation,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :universeIsType,
Error :productIsType,
axiomSqEquality
Latex:
\mforall{}[as:Top List]. \mforall{}[f:Top]. last(map(f;as)) \msim{} f last(as) supposing \mneg{}\muparrow{}null(as)
Date html generated:
2019_06_20-PM-01_33_44
Last ObjectModification:
2018_10_06-AM-11_23_20
Theory : list_1
Home
Index