Nuprl Lemma : uniform-continuity-pi-search_wf
∀[n:ℕ]. ∀[G:∀m:ℕn. (Top + Top)]. ∀[x:ℕ]. (uniform-continuity-pi-search(G;n;x) ∈ ℕ)
Proof
Definitions occuring in Statement :
uniform-continuity-pi-search: uniform-continuity-pi-search,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
top: Top,
all: ∀x:A. B[x],
member: t ∈ T,
union: left + right,
natural_number: $n
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
sq_type: SQType(T),
guard: {T},
uniform-continuity-pi-search: uniform-continuity-pi-search,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
bnot: ¬bb,
assert: ↑b,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
subtract: n - m
Lemmas referenced :
decidable__lt,
nat_wf,
all_wf,
int_seg_wf,
top_wf,
subtract_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
le_wf,
decidable__equal_int,
intformeq_wf,
itermAdd_wf,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
equal_wf,
subtype_base_sq,
int_subtype_base,
ge_wf,
less_than_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
isl_wf,
lelt_wf,
add-commutes,
add-associates,
add-swap,
zero-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
because_Cache,
unionElimination,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
isectElimination,
natural_numberEquality,
lambdaEquality,
unionEquality,
dependent_pairFormation,
dependent_set_memberEquality,
independent_isectElimination,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
addEquality,
productElimination,
instantiate,
cumulativity,
independent_functionElimination,
intWeakElimination,
lambdaFormation,
equalityElimination,
promote_hyp,
applyEquality,
functionExtensionality,
applyLambdaEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[G:\mforall{}m:\mBbbN{}n. (Top + Top)]. \mforall{}[x:\mBbbN{}]. (uniform-continuity-pi-search(G;n;x) \mmember{} \mBbbN{})
Date html generated:
2017_04_17-AM-09_58_36
Last ObjectModification:
2017_02_27-PM-05_51_51
Theory : continuity
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