Nuprl Lemma : fan-realizer_test
∃k:ℕ. ∀f:ℕ ⟶ 𝔹. ∃n:ℕk. ((λl.(3 ≤ ||l||)) map(f;upto(n)))
Proof
Definitions occuring in Statement :
upto: upto(n),
length: ||as||,
map: map(f;as),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
le: A ≤ B,
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
tbar: tbar(T;X),
all: ∀x:A. B[x],
dec-predicate: Decidable(X),
exists: ∃x:A. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
prop: ℙ,
squash: ↓T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
map_wf,
length_upto,
iff_weakening_equal,
upto_wf,
subtype_rel_self,
int_seg_subtype_nat,
subtype_rel_dep_function,
int_seg_wf,
map_length_nat,
true_wf,
squash_wf,
false_wf,
decidable__le,
nat_wf,
list_wf,
bool_wf,
length_wf,
le_wf,
fan-realizer_wf
Rules used in proof :
cut,
lemma_by_obid,
comment,
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalHypSubstitution,
equalityTransitivity,
hypothesis,
equalitySymmetry,
isectElimination,
thin,
lambdaEquality,
natural_numberEquality,
hypothesisEquality,
independent_functionElimination,
sqequalRule,
lambdaFormation,
functionEquality,
dependent_functionElimination,
dependent_pairFormation,
dependent_set_memberEquality,
independent_pairFormation,
applyEquality,
imageElimination,
intEquality,
because_Cache,
independent_isectElimination,
setElimination,
rename,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination
Latex:
\mexists{}k:\mBbbN{}. \mforall{}f:\mBbbN{} {}\mrightarrow{} \mBbbB{}. \mexists{}n:\mBbbN{}k. ((\mlambda{}l.(3 \mleq{} ||l||)) map(f;upto(n)))
Date html generated:
2016_05_15-PM-10_05_26
Last ObjectModification:
2016_01_16-PM-04_05_34
Theory : bar!induction
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