Nuprl Lemma : polymorphic-list
∀f:⋂A:Type. (A ⟶ (A List)). ∃n:ℕ. (f = (λx.repn(n;x)) ∈ (⋂A:Type. (A ⟶ (A List))))
Proof
Definitions occuring in Statement :
repn: repn(n;x),
list: T List,
nat: ℕ,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
lambda: λx.A[x],
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
exists: ∃x:A. B[x],
prop: ℙ,
uimplies: b supposing a,
int_seg: {i..j-},
guard: {T},
nat: ℕ,
ge: i ≥ j ,
lelt: i ≤ j < k,
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
squash: ↓T,
true: True,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
polymorphic-constant-nat,
length_wf_nat,
list_wf,
equal_wf,
repn_wf,
subtype_rel_list,
polymorphic-id-unique-sq,
select_wf,
int_seg_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
intformeq_wf,
int_formula_prop_less_lemma,
int_formula_prop_eq_lemma,
int_seg_wf,
list_extensionality,
less_than_wf,
length_wf,
nat_wf,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal,
length-repn,
lelt_wf,
select-repn
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
lambdaEquality,
isectElimination,
hypothesisEquality,
applyEquality,
equalityTransitivity,
equalitySymmetry,
hypothesis,
isectEquality,
universeEquality,
cumulativity,
functionEquality,
sqequalRule,
productElimination,
dependent_pairFormation,
instantiate,
setEquality,
independent_isectElimination,
setElimination,
rename,
because_Cache,
natural_numberEquality,
unionElimination,
approximateComputation,
independent_functionElimination,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
applyLambdaEquality,
functionExtensionality,
imageElimination,
imageMemberEquality,
baseClosed,
dependent_set_memberEquality
Latex:
\mforall{}f:\mcap{}A:Type. (A {}\mrightarrow{} (A List)). \mexists{}n:\mBbbN{}. (f = (\mlambda{}x.repn(n;x)))
Date html generated:
2018_05_21-PM-01_12_02
Last ObjectModification:
2018_05_01-PM-04_37_01
Theory : num_thy_1
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