Nuprl Lemma : list_accum'_wf
∀[A,B:Type].
∀[f:B ⟶ {L:A List| 0 < ||L||} ⟶ B]. ∀[L:A List]. ∀[v:B]. (list_accum'(f;v;L) ∈ B) supposing valueall-type(B)
Proof
Definitions occuring in Statement :
list_accum': list_accum'(f;v;L),
length: ||as||,
list: T List,
valueall-type: valueall-type(T),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
nat_plus: ℕ+,
has-valueall: has-valueall(a),
has-value: (a)↓,
callbyvalueall: callbyvalueall,
exists: ∃x:A. B[x],
bfalse: ff,
less_than: a < b,
sq_type: SQType(T),
so_apply: x[s],
so_lambda: λ2x.t[x],
it: ⋅,
nil: [],
subtract: n - m,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
decidable: Dec(P),
true: True,
less_than': less_than'(a;b),
not: ¬A,
le: A ≤ B,
and: P ∧ Q,
uiff: uiff(P;Q),
sq_stable: SqStable(P),
squash: ↓T,
so_apply: x[s1;s2],
top: Top,
so_lambda: λ2x y.t[x; y],
colength: colength(L),
cons: [a / b],
btrue: tt,
ifthenelse: if b then t else f fi ,
list_accum': list_accum'(f;v;L),
or: P ∨ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T},
ge: i ≥ j ,
false: False,
implies: P ⇒ Q,
nat: ℕ,
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
decidable__lt,
omega-shadow,
minus-zero,
not-lt-2,
zero-mul,
mul-distributes-right,
two-mul,
add-mul-special,
one-mul,
le_reflexive,
valueall-type_wf,
list_wf,
evalall-reduce,
length_wf,
cons_wf,
length_wf_nat,
non_neg_length,
length_of_cons_lemma,
valueall-type-has-valueall,
null_cons_lemma,
int_subtype_base,
set_subtype_base,
subtype_base_sq,
add-swap,
minus-minus,
less-iff-le,
not-ge-2,
subtract_wf,
equal_wf,
le_wf,
add-commutes,
minus-one-mul-top,
minus-one-mul,
minus-add,
condition-implies-le,
not-le-2,
false_wf,
decidable__le,
le-add-cancel,
zero-add,
add-zero,
add-associates,
add_functionality_wrt_le,
le_antisymmetry_iff,
sq_stable__le,
spread_cons_lemma,
product_subtype_list,
null_nil_lemma,
list-cases,
colength_wf_list,
nat_wf,
equal-wf-T-base,
less_than_wf,
ge_wf,
less_than_irreflexivity,
less_than_transitivity1,
nat_properties
Rules used in proof :
multiplyEquality,
universeEquality,
setEquality,
functionEquality,
callbyvalueReduce,
sqequalIntensionalEquality,
dependent_pairFormation,
functionExtensionality,
instantiate,
intEquality,
minusEquality,
independent_pairFormation,
dependent_set_memberEquality,
addEquality,
imageElimination,
baseClosed,
imageMemberEquality,
applyLambdaEquality,
voidEquality,
productElimination,
hypothesis_subsumption,
promote_hyp,
unionElimination,
because_Cache,
applyEquality,
cumulativity,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
isect_memberEquality,
dependent_functionElimination,
lambdaEquality,
voidElimination,
independent_functionElimination,
independent_isectElimination,
natural_numberEquality,
intWeakElimination,
sqequalRule,
rename,
setElimination,
hypothesis,
hypothesisEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaFormation,
thin,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A,B:Type].
\mforall{}[f:B {}\mrightarrow{} \{L:A List| 0 < ||L||\} {}\mrightarrow{} B]. \mforall{}[L:A List]. \mforall{}[v:B]. (list\_accum'(f;v;L) \mmember{} B)
supposing valueall-type(B)
Date html generated:
2017_04_14-AM-08_48_31
Last ObjectModification:
2017_04_10-PM-10_33_51
Theory : list_0
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