Nuprl Lemma : sphere-map-eq_wf
∀[n:ℕ]. ∀[f,g:S(n) ⟶ S(n)]. (sphere-map-eq(n;f;g) ∈ ℙ)
Proof
Definitions occuring in Statement :
sphere-map-eq: sphere-map-eq(n;f;g),
real-unit-sphere: S(n),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
sphere-map-eq: sphere-map-eq(n;f;g),
prop: ℙ,
all: ∀x:A. B[x],
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),
exists: ∃x:A. B[x],
false: False,
top: Top,
and: P ∧ Q,
subtype_rel: A ⊆r B,
real-unit-sphere: S(n)
Lemmas referenced :
real-unit-sphere_wf,
req-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,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_set_memberEquality_alt,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
applyEquality,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isectIsTypeImplies,
functionIsType
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[f,g:S(n) {}\mrightarrow{} S(n)]. (sphere-map-eq(n;f;g) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-10_15_27
Last ObjectModification:
2019_07_30-PM-02_18_13
Theory : real!vectors
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