Nuprl Lemma : partial_ap_gen_wf
∀[T:Type]. ∀[n:ℕ]. ∀[s:ℕn + 1]. ∀[m:ℕ(n - s) + 1]. ∀[A:ℕn ⟶ Type]. ∀[g:funtype(n;A;T) ⟶ T].
(partial_ap_gen(g;n;s;m) ∈ funtype(m;λi.(A (s + i));T) ⟶ T)
Proof
Definitions occuring in Statement :
partial_ap_gen: partial_ap_gen(g;n;s;m),
funtype: funtype(n;A;T),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
subtract: n - m,
add: n + m,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
partial_ap_gen: partial_ap_gen(g;n;s;m),
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
int_seg: {i..j-},
guard: {T},
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
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],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
uiff: uiff(P;Q),
le: A ≤ B,
less_than: a < b,
subtype_rel: A ⊆r B,
less_than': less_than'(a;b),
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
squash: ↓T,
true: True
Lemmas referenced :
nat_wf,
ext-eq_weakening,
subtype_rel_weakening,
add-commutes,
subtype_rel-equal,
mk_lambdas_fun_wf,
int_subtype_base,
subtype_base_sq,
equal_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
decidable__equal_int,
subtype_rel_self,
int_seg_subtype,
subtype_rel_dep_function,
false_wf,
int_seg_subtype_nat,
int_seg_wf,
lelt_wf,
decidable__lt,
add-member-int_seg1,
le_wf,
int_formula_prop_wf,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermAdd_wf,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
int_seg_properties,
subtract_wf,
funtype_wf,
mk_lambdas_wf,
funtype-split
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaEquality,
applyEquality,
hypothesisEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_set_memberEquality,
setElimination,
rename,
hypothesis,
natural_numberEquality,
addEquality,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
lambdaFormation,
instantiate,
cumulativity,
universeEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
imageElimination,
functionExtensionality,
imageMemberEquality,
baseClosed,
functionEquality,
introduction,
isect_memberFormation,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[s:\mBbbN{}n + 1]. \mforall{}[m:\mBbbN{}(n - s) + 1]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[g:funtype(n;A;T) {}\mrightarrow{} T].
(partial\_ap\_gen(g;n;s;m) \mmember{} funtype(m;\mlambda{}i.(A (s + i));T) {}\mrightarrow{} T)
Date html generated:
2016_05_15-PM-02_10_09
Last ObjectModification:
2016_01_15-PM-10_23_55
Theory : untyped!computation
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