Nuprl Lemma : unit-ball-approx0
∀[k:ℕ]. unit-ball-approx(0;k) ≡ Top
Proof
Definitions occuring in Statement :
unit-ball-approx: unit-ball-approx(n;k),
nat: ℕ,
ext-eq: A ≡ B,
uall: ∀[x:A]. B[x],
top: Top,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
top: Top,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
implies: P ⇒ Q,
false: False,
unit-ball-approx: unit-ball-approx(n;k),
sum: Σ(f[x] | x < k),
sum_aux: sum_aux(k;v;i;x.f[x]),
int_seg: {i..j-},
lelt: i ≤ j < k,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
prop: ℙ
Lemmas referenced :
istype-void,
unit-ball-approx_wf,
istype-le,
int_seg_properties,
nat_properties,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
int_seg_wf,
mul_bounds_1a,
istype-top,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
independent_pairFormation,
lambdaEquality_alt,
isect_memberEquality_alt,
voidElimination,
extract_by_obid,
hypothesis,
universeIsType,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality_alt,
natural_numberEquality,
sqequalRule,
lambdaFormation_alt,
hypothesisEquality,
functionExtensionality,
setElimination,
rename,
productElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
dependent_functionElimination,
multiplyEquality,
because_Cache,
independent_pairEquality,
axiomEquality,
applyEquality
Latex:
\mforall{}[k:\mBbbN{}]. unit-ball-approx(0;k) \mequiv{} Top
Date html generated:
2019_10_30-AM-11_28_04
Last ObjectModification:
2019_07_30-AM-11_25_27
Theory : real!vectors
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