Nuprl Lemma : m-regularize_wf
∀[X:Type]. ∀[d:metric(X)]. ∀[s:ℕ ⟶ X]. (m-regularize(d;s) ∈ ℕ ⟶ X)
Proof
Definitions occuring in Statement :
m-regularize: m-regularize(d;s),
metric: metric(X),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
int_seg: {i..j-},
lelt: i ≤ j < k
Lemmas referenced :
m-regularize_wf_finite,
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,
subtype_rel_function,
int_seg_wf,
int_seg_subtype_nat,
istype-false,
subtype_rel_self,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-less_than,
nat_wf,
istype-nat,
metric_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
functionExtensionality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality_alt,
addEquality,
setElimination,
rename,
hypothesis,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
sqequalRule,
independent_pairFormation,
universeIsType,
applyEquality,
because_Cache,
lambdaFormation_alt,
productIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
isectIsTypeImplies,
inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[X:Type]. \mforall{}[d:metric(X)]. \mforall{}[s:\mBbbN{} {}\mrightarrow{} X]. (m-regularize(d;s) \mmember{} \mBbbN{} {}\mrightarrow{} X)
Date html generated:
2019_10_30-AM-07_03_20
Last ObjectModification:
2019_10_03-PM-06_06_02
Theory : reals
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