Nuprl Lemma : uncurry-gen_wf
∀[B:Type]. ∀[n:ℕ]. ∀[m:ℕn + 1]. ∀[A:ℕn ⟶ Type]. ∀[g:(k:ℕn ⟶ (A k)) ⟶ funtype(n - m;λx.(A (x + m));B)].
(uncurry-gen(n) m g ∈ (k:ℕn ⟶ (A k)) ⟶ B)
Proof
Definitions occuring in Statement :
uncurry-gen: uncurry-gen(n),
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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
uiff: uiff(P;Q),
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
uncurry-gen: uncurry-gen(n),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
funtype: funtype(n;A;T),
primrec: primrec(n;b;c),
less_than: a < b,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
le: A ≤ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
nat_properties,
full-omega-unsat,
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,
funtype_wf,
int_seg_properties,
itermSubtract_wf,
int_term_value_subtract_lemma,
add-member-int_seg2,
lelt_wf,
subtract_wf,
le_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
decidable__equal_int,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
intformeq_wf,
int_formula_prop_eq_lemma,
decidable__lt,
subtype_rel_self,
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
subtype_rel-equal,
lt_int_wf,
assert_of_lt_int,
top_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
nequal-le-implies,
itermAdd_wf,
int_term_value_add_lemma,
int_seg_subtype_nat,
false_wf,
add-member-int_seg1,
nat_wf,
funtype-unroll,
assert_wf,
bnot_wf,
not_wf,
equal-wf-T-base,
zero-add,
add-is-int-iff,
add-associates,
add-swap,
add-commutes,
bool_cases,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
because_Cache,
applyEquality,
functionExtensionality,
cumulativity,
productElimination,
dependent_set_memberEquality,
universeEquality,
unionElimination,
instantiate,
applyLambdaEquality,
hypothesis_subsumption,
equalityElimination,
lessCases,
baseClosed,
imageMemberEquality,
axiomSqEquality,
imageElimination,
promote_hyp,
addEquality,
baseApply,
closedConclusion
Latex:
\mforall{}[B:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[m:\mBbbN{}n + 1]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type].
\mforall{}[g:(k:\mBbbN{}n {}\mrightarrow{} (A k)) {}\mrightarrow{} funtype(n - m;\mlambda{}x.(A (x + m));B)].
(uncurry-gen(n) m g \mmember{} (k:\mBbbN{}n {}\mrightarrow{} (A k)) {}\mrightarrow{} B)
Date html generated:
2019_10_15-AM-11_04_15
Last ObjectModification:
2018_08_25-PM-02_15_10
Theory : bags
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