Nuprl Lemma : simple-cbva-seq_wf
∀[T:Type]. ∀[m:ℕ]. ∀[A:ℕm ⟶ ValueAllType]. ∀[L:i:ℕm ⟶ funtype(i;A;A i)]. ∀[F:if (m =z 0)
then T
else (A (m - 1)) ⟶ T
fi ].
(simple-cbva-seq(L;F;m) ∈ T)
Proof
Definitions occuring in Statement :
simple-cbva-seq: simple-cbva-seq(L;F;m),
funtype: funtype(n;A;T),
int_seg: {i..j-},
nat: ℕ,
vatype: ValueAllType,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
subtract: n - m,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
vatype: ValueAllType,
simple-cbva-seq: simple-cbva-seq(L;F;m),
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
subtype_rel: A ⊆r B,
funtype: funtype(n;A;T),
int_seg: {i..j-},
ge: i ≥ j ,
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
squash: ↓T,
decidable: Dec(P),
or: P ∨ Q,
true: True,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
int_upper: {i...},
so_lambda: λ2x.t[x],
so_apply: x[s],
le: A ≤ B,
less_than': less_than'(a;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
nequal: a ≠ b ∈ T
Lemmas referenced :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
cbva-seq_wf,
subtype_rel-equal,
primrec_wf,
int_seg_properties,
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermVar_wf,
intformle_wf,
itermConstant_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
primrec0_lemma,
squash_wf,
true_wf,
int_seg_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
le_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_upper_subtype_nat,
nequal-le-implies,
zero-add,
mk_lambdas_wf,
subtype_rel_dep_function,
valueall-type_wf,
subtract_wf,
int_seg_subtype,
int_upper_properties,
itermSubtract_wf,
int_term_value_subtract_lemma,
false_wf,
decidable__lt,
lelt_wf,
funtype_wf,
int_seg_subtype_nat,
nat_wf,
subtype_rel_wf,
funtype-unroll-last-eq,
iff_weakening_equal,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
because_Cache,
hypothesis,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
sqequalRule,
cumulativity,
hypothesisEquality,
functionExtensionality,
applyEquality,
instantiate,
universeEquality,
lambdaEquality,
functionEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
dependent_set_memberEquality,
imageMemberEquality,
baseClosed,
promote_hyp,
independent_functionElimination,
hypothesis_subsumption,
setEquality,
isect_memberFormation,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[m:\mBbbN{}]. \mforall{}[A:\mBbbN{}m {}\mrightarrow{} ValueAllType]. \mforall{}[L:i:\mBbbN{}m {}\mrightarrow{} funtype(i;A;A i)]. \mforall{}[F:if (m =\msubz{} 0)
then T
else (A (m - 1)) {}\mrightarrow{} T
fi ].
(simple-cbva-seq(L;F;m) \mmember{} T)
Date html generated:
2017_10_01-AM-08_41_07
Last ObjectModification:
2017_07_26-PM-04_28_25
Theory : untyped!computation
Home
Index