Nuprl Lemma : id-sphere-map_wf
∀[n:ℕ]. (id-sphere-map() ∈ sphere-map(n))
Proof
Definitions occuring in Statement :
id-sphere-map: id-sphere-map(),
sphere-map: sphere-map(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sphere-map: sphere-map(n),
id-sphere-map: id-sphere-map(),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
nat: ℕ,
nat_plus: ℕ+,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
and: P ∧ Q,
prop: ℙ,
real-unit-sphere: S(n),
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
rneq: x ≠ y,
guard: {T}
Lemmas referenced :
real-unit-sphere_wf,
rleq_wf,
real-vec-dist_wf,
nat_plus_properties,
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,
rdiv_wf,
rneq-int,
nat_plus_wf,
int-to-real_wf,
rless-int,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
rless_wf,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
hypothesisEquality,
universeIsType,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
sqequalRule,
lambdaFormation_alt,
dependent_pairFormation_alt,
addEquality,
setElimination,
rename,
because_Cache,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
applyEquality,
productElimination,
inhabitedIsType,
functionIsType,
productIsType,
closedConclusion,
inrFormation_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}]. (id-sphere-map() \mmember{} sphere-map(n))
Date html generated:
2019_10_30-AM-10_15_36
Last ObjectModification:
2019_07_30-PM-02_28_04
Theory : real!vectors
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