Nuprl Lemma : const-sphere-map_wf
∀[n:ℕ]. ∀[p:S(n)]. (const-sphere-map(p) ∈ sphere-map(n))
Proof
Definitions occuring in Statement :
const-sphere-map: const-sphere-map(p),
sphere-map: sphere-map(n),
real-unit-sphere: S(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),
const-sphere-map: const-sphere-map(p),
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
nat_plus: ℕ+,
nat: ℕ,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
prop: ℙ,
false: False,
and: P ∧ Q,
real-unit-sphere: S(n),
subtype_rel: A ⊆r B,
rneq: x ≠ y,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
nat_plus_properties,
nat_properties,
decidable__lt,
full-omega-unsat,
intformnot_wf,
intformless_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-less_than,
real-vec-dist-same-zero,
decidable__le,
intformand_wf,
intformle_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
istype-le,
rleq_wf,
real-vec-dist_wf,
rdiv_wf,
int-to-real_wf,
rless-int,
rless_wf,
nat_plus_wf,
real-unit-sphere_wf,
istype-nat,
rleq-int-fractions2,
itermMultiply_wf,
int_term_value_mul_lemma,
rleq_functionality,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
hypothesisEquality,
inhabitedIsType,
sqequalRule,
lambdaFormation_alt,
dependent_pairFormation_alt,
natural_numberEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
isect_memberEquality_alt,
voidElimination,
universeIsType,
addEquality,
because_Cache,
int_eqEquality,
independent_pairFormation,
applyEquality,
closedConclusion,
inrFormation_alt,
productElimination,
imageMemberEquality,
baseClosed,
functionIsType,
productIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectIsTypeImplies,
multiplyEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[p:S(n)]. (const-sphere-map(p) \mmember{} sphere-map(n))
Date html generated:
2019_10_30-AM-10_15_31
Last ObjectModification:
2019_07_30-PM-02_25_26
Theory : real!vectors
Home
Index