Nuprl Lemma : strong-continuity-test_wf
∀[T:Type]. ∀[M:n:ℕ ⟶ (ℕn ⟶ T) ⟶ (ℕ?)]. ∀[n:ℕ]. ∀[f:ℕn ⟶ T]. ∀[b:ℕ?]. (strong-continuity-test(M;n;f;b) ∈ ℕ?)
Proof
Definitions occuring in Statement :
strong-continuity-test: strong-continuity-test(M;n;f;b),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
and: P ∧ Q,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
strong-continuity-test: strong-continuity-test(M;n;f;b),
lelt: i ≤ j < k,
int_seg: {i..j-},
assert: ↑b,
bnot: ¬bb,
guard: {T},
sq_type: SQType(T),
bfalse: ff,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
exposed-it: exposed-it,
less_than': less_than'(a;b),
le: A ≤ B,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B
Lemmas referenced :
nat_wf,
unit_wf2,
int_seg_wf,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
less_than_wf,
decidable__le,
subtract_wf,
intformnot_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
primrec0_lemma,
int_seg_properties,
int_seg_subtype_nat,
primrec_wf,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
eqtt_to_assert,
bool_wf,
false_wf,
int_seg_subtype,
subtype_rel_dep_function,
le_wf,
satisfiable-full-omega-tt,
isl_wf,
primrec-unroll-1
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
unionEquality,
cut,
introduction,
extract_by_obid,
hypothesis,
because_Cache,
functionEquality,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
universeEquality,
isect_memberFormation,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
intWeakElimination,
lambdaFormation,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
voidElimination,
voidEquality,
independent_pairFormation,
unionElimination,
cumulativity,
instantiate,
promote_hyp,
inrEquality,
productElimination,
equalityElimination,
computeAll,
functionExtensionality,
applyEquality,
dependent_set_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[M:n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} (\mBbbN{}?)]. \mforall{}[n:\mBbbN{}]. \mforall{}[f:\mBbbN{}n {}\mrightarrow{} T]. \mforall{}[b:\mBbbN{}?].
(strong-continuity-test(M;n;f;b) \mmember{} \mBbbN{}?)
Date html generated:
2019_06_20-PM-02_49_59
Last ObjectModification:
2018_09_26-AM-09_54_20
Theory : continuity
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