Nuprl Lemma : mk_lambdas_fun_wf
∀[T,U:Type]. ∀[m:ℕ]. ∀[A:ℕm ⟶ Type]. ∀[F:(funtype(m;A;T) ⟶ T) ⟶ U]. (mk_lambdas_fun(F;m) ∈ funtype(m;A;U))
Proof
Definitions occuring in Statement :
mk_lambdas_fun: mk_lambdas_fun(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_fun: mk_lambdas_fun(F;m),
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
subtype_rel: A ⊆r B,
funtype: funtype(n;A;T),
primrec: primrec(n;b;c),
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
uiff: uiff(P;Q),
subtract: n - m,
squash: ↓T,
less_than: a < b,
true: True
Lemmas referenced :
nat_wf,
add-zero,
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int,
add-member-int_seg2,
int_term_value_subtract_lemma,
itermSubtract_wf,
subtract_wf,
subtype_rel-equal,
int_seg_properties,
decidable__le,
int_seg_subtype,
int_seg_wf,
subtype_rel_dep_function,
le_wf,
funtype_wf,
subtype_rel_self,
lelt_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_properties,
false_wf,
mk_lambdas-fun_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
addEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
applyEquality,
because_Cache,
instantiate,
universeEquality,
productElimination,
imageElimination,
functionExtensionality,
imageMemberEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[T,U:Type]. \mforall{}[m:\mBbbN{}]. \mforall{}[A:\mBbbN{}m {}\mrightarrow{} Type]. \mforall{}[F:(funtype(m;A;T) {}\mrightarrow{} T) {}\mrightarrow{} U].
(mk\_lambdas\_fun(F;m) \mmember{} funtype(m;A;U))
Date html generated:
2016_05_15-PM-02_09_51
Last ObjectModification:
2016_01_15-PM-10_21_52
Theory : untyped!computation
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