Nuprl Lemma : fan-realizer_test2
∀m:ℕ. ∃k:ℕ. ∀f:ℕ ⟶ 𝔹. ∃n:ℕk. ((λl.(m ≤ ||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,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
tbar: tbar(T;X),
exists: ∃x:A. B[x],
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
dec-predicate: Decidable(X)
Lemmas referenced :
map_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
intformle_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
length_upto,
iff_weakening_equal,
upto_wf,
subtype_rel_self,
false_wf,
int_seg_subtype_nat,
subtype_rel_dep_function,
int_seg_wf,
map_length_nat,
true_wf,
squash_wf,
list_wf,
bool_wf,
length_wf,
le_wf,
nat_wf,
fan-realizer_wf
Rules used in proof :
cut,
lemma_by_obid,
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
sqequalHypSubstitution,
equalityTransitivity,
hypothesis,
equalitySymmetry,
lambdaFormation,
isectElimination,
thin,
lambdaEquality,
setElimination,
rename,
hypothesisEquality,
independent_functionElimination,
sqequalRule,
dependent_pairFormation,
applyEquality,
imageElimination,
intEquality,
natural_numberEquality,
independent_isectElimination,
independent_pairFormation,
because_Cache,
imageMemberEquality,
baseClosed,
universeEquality,
productElimination,
dependent_functionElimination,
unionElimination,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
functionEquality
Latex:
\mforall{}m:\mBbbN{}. \mexists{}k:\mBbbN{}. \mforall{}f:\mBbbN{} {}\mrightarrow{} \mBbbB{}. \mexists{}n:\mBbbN{}k. ((\mlambda{}l.(m \mleq{} ||l||)) map(f;upto(n)))
Date html generated:
2016_05_15-PM-10_05_29
Last ObjectModification:
2016_01_16-PM-04_05_33
Theory : bar!induction
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