Nuprl Lemma : seq-cont_wf
∀[T:Type]. ∀[F:(ℕ ⟶ T) ⟶ ℕ]. (seq-cont(T;F) ∈ ℙ)
Proof
Definitions occuring in Statement :
seq-cont: seq-cont(T;F),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
uimplies: b supposing a,
so_apply: x[s],
subtype_rel: A ⊆r B,
nat: ℕ,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
seq-cont: seq-cont(T;F),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
false_wf,
int_seg_subtype_nat,
subtype_rel_dep_function,
int_upper_subtype_nat,
int_seg_wf,
equal_wf,
int_upper_wf,
exists_wf,
nat_wf,
all_wf
Rules used in proof :
universeEquality,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
lambdaFormation,
independent_pairFormation,
independent_isectElimination,
functionExtensionality,
applyEquality,
natural_numberEquality,
rename,
setElimination,
because_Cache,
lambdaEquality,
hypothesisEquality,
cumulativity,
hypothesis,
functionEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[F:(\mBbbN{} {}\mrightarrow{} T) {}\mrightarrow{} \mBbbN{}]. (seq-cont(T;F) \mmember{} \mBbbP{})
Date html generated:
2017_09_29-PM-06_05_45
Last ObjectModification:
2017_07_19-AM-10_22_51
Theory : continuity
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