Nuprl Lemma : mk_lambdas_wf
∀[T:Type]. ∀[m:ℕ]. ∀[A:ℕm ⟶ Type]. ∀[F:T]. (mk_lambdas(F;m) ∈ funtype(m;A;T))
Proof
Definitions occuring in Statement :
mk_lambdas: mk_lambdas(F;m),
funtype: funtype(n;A;T),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
mk_lambdas: mk_lambdas(F;m),
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
funtype: funtype(n;A;T),
decidable: Dec(P),
or: P ∨ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
int_seg: {i..j-},
lelt: i ≤ j < k,
nequal: a ≠ b ∈ T ,
subtract: n - m,
le: A ≤ B,
less_than: a < b,
subtype_rel: A ⊆r B,
squash: ↓T,
true: True
Lemmas referenced :
nat_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
int_seg_wf,
primrec0_lemma,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
nat_wf,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
add-member-int_seg2,
lelt_wf,
subtype_rel-equal,
primrec_wf,
le_wf,
int_seg_properties,
itermAdd_wf,
int_term_value_add_lemma,
decidable__lt,
decidable__equal_int,
intformeq_wf,
int_formula_prop_eq_lemma,
add-associates,
minus-one-mul,
add-swap,
add-commutes,
itermMultiply_wf,
int_term_value_mul_lemma,
primrec-unroll
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
lambdaFormation,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
unionElimination,
because_Cache,
equalityElimination,
productElimination,
promote_hyp,
instantiate,
applyEquality,
functionExtensionality,
dependent_set_memberEquality,
addEquality,
imageElimination,
multiplyEquality,
minusEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[T:Type]. \mforall{}[m:\mBbbN{}]. \mforall{}[A:\mBbbN{}m {}\mrightarrow{} Type]. \mforall{}[F:T]. (mk\_lambdas(F;m) \mmember{} funtype(m;A;T))
Date html generated:
2017_10_01-AM-08_40_04
Last ObjectModification:
2017_07_26-PM-04_27_52
Theory : untyped!computation
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