Nuprl Lemma : real-unit-ball-0
B(0) ≡ Top
Proof
Definitions occuring in Statement :
real-unit-ball: B(n)
,
ext-eq: A ≡ B
,
top: Top
,
natural_number: $n
Definitions unfolded in proof :
ext-eq: A ≡ B
,
and: P ∧ Q
,
subtype_rel: A ⊆r B
,
member: t ∈ T
,
top: Top
,
uall: ∀[x:A]. B[x]
,
nat: ℕ
,
le: A ≤ B
,
less_than': less_than'(a;b)
,
not: ¬A
,
implies: P
⇒ Q
,
false: False
,
real-unit-ball: B(n)
,
real-vec: ℝ^n
,
int_seg: {i..j-}
,
lelt: i ≤ j < k
,
uimplies: b supposing a
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
,
all: ∀x:A. B[x]
,
prop: ℙ
,
real-vec-norm: ||x||
,
dot-product: x⋅y
,
subtract: n - m
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
,
less_than: a < b
,
squash: ↓T
,
true: True
,
iff: P
⇐⇒ Q
,
rev_implies: P
⇐ Q
,
uiff: uiff(P;Q)
,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
istype-void,
real-unit-ball_wf,
istype-le,
int_seg_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,
rleq_wf,
real-vec-norm_wf,
int-to-real_wf,
istype-top,
rsum-empty,
rsqrt_wf,
rleq_weakening_equal,
rleq-int,
istype-false,
rleq_functionality,
rsqrt0,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
independent_pairFormation,
lambdaEquality_alt,
isect_memberEquality_alt,
voidElimination,
cut,
introduction,
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,
minusEquality,
imageMemberEquality,
baseClosed,
because_Cache,
applyEquality
Latex:
B(0) \mequiv{} Top
Date html generated:
2019_10_30-AM-10_15_12
Last ObjectModification:
2019_06_28-PM-01_52_18
Theory : real!vectors
Home
Index