Nuprl Lemma : callbyvalueall_seq_wf
∀[T,U:Type]. ∀[m:ℕ]. ∀[n:ℕm + 1]. ∀[A:ℕm ⟶ ValueAllType]. ∀[L:i:ℕm ⟶ funtype(i;A;A i)]. ∀[G:∀[T:Type]
(funtype(n;A;T) ⟶ T)].
∀[F:(funtype(m;A;T) ⟶ T) ⟶ U].
(callbyvalueall_seq(L;G;F;n;m) ∈ U)
Proof
Definitions occuring in Statement :
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
funtype: funtype(n;A;T),
int_seg: {i..j-},
nat: ℕ,
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
vatype: ValueAllType,
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
int_seg: {i..j-},
exists: ∃x:A. B[x],
lelt: i ≤ j < k,
and: P ∧ Q,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
sq_type: SQType(T),
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
callbyvalueall_seq: callbyvalueall_seq(L;G;F;n;m),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
le: A ≤ B,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtract: n - m,
true: True,
sq_stable: SqStable(P),
squash: ↓T,
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a)
Lemmas referenced :
int_seg_properties,
subtract_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
le_wf,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
equal-wf-base-T,
int_subtype_base,
subtype_base_sq,
ge_wf,
less_than_wf,
uall_wf,
funtype_wf,
less_than_transitivity1,
less_than_irreflexivity,
lelt_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
int_seg_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
subtype_rel_dep_function,
valueall-type_wf,
int_seg_subtype,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-mul-special,
zero-mul,
add-zero,
minus-zero,
add-associates,
zero-add,
add-commutes,
le-add-cancel,
decidable__lt,
less-iff-le,
minus-minus,
add_functionality_wrt_le,
two-mul,
le-add-cancel2,
int_seg_subtype_nat,
sq_stable__le,
le_weakening2,
nat_wf,
valueall-type-has-valueall,
sq_stable__valueall-type,
evalall-reduce,
member_wf,
squash_wf,
true_wf,
funtype-unroll-last-eq,
iff_weakening_equal,
add-subtract-cancel,
eq_int_wf,
assert_wf,
bnot_wf,
not_wf,
equal-wf-T-base,
bool_cases,
assert_of_eq_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
addEquality,
setElimination,
rename,
because_Cache,
hypothesis,
hypothesisEquality,
dependent_pairFormation,
productElimination,
dependent_set_memberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
applyEquality,
promote_hyp,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
intWeakElimination,
lambdaFormation,
axiomEquality,
universeEquality,
functionEquality,
equalityElimination,
isectEquality,
functionExtensionality,
setEquality,
minusEquality,
multiplyEquality,
imageMemberEquality,
baseClosed,
imageElimination,
callbyvalueReduce
Latex:
\mforall{}[T,U:Type]. \mforall{}[m:\mBbbN{}]. \mforall{}[n:\mBbbN{}m + 1]. \mforall{}[A:\mBbbN{}m {}\mrightarrow{} ValueAllType]. \mforall{}[L:i:\mBbbN{}m {}\mrightarrow{} funtype(i;A;A i)].
\mforall{}[G:\mforall{}[T:Type]. (funtype(n;A;T) {}\mrightarrow{} T)]. \mforall{}[F:(funtype(m;A;T) {}\mrightarrow{} T) {}\mrightarrow{} U].
(callbyvalueall\_seq(L;G;F;n;m) \mmember{} U)
Date html generated:
2019_10_15-AM-10_58_45
Last ObjectModification:
2018_08_25-PM-02_13_41
Theory : untyped!computation
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