Nuprl Lemma : real-unit-sphere-subtype-ball
∀[n:ℕ]. (S(n) ⊆r B(n + 1))
Proof
Definitions occuring in Statement :
real-unit-sphere: S(n),
real-unit-ball: B(n),
nat: ℕ,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
real-unit-sphere: S(n),
real-unit-ball: B(n),
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_sets_simple,
real-vec_wf,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
req_wf,
real-vec-norm_wf,
int-to-real_wf,
rleq_wf,
rleq_weakening,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality_alt,
addEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
because_Cache,
lambdaFormation_alt,
axiomEquality
Latex:
\mforall{}[n:\mBbbN{}]. (S(n) \msubseteq{}r B(n + 1))
Date html generated:
2019_10_30-AM-10_15_19
Last ObjectModification:
2019_07_30-AM-09_21_44
Theory : real!vectors
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