Nuprl Lemma : uniform-continuity-pi_wf
∀[T:Type]. ∀[F:(ℕ ⟶ 𝔹) ⟶ T]. ∀[n:ℕ]. (ucA(T;F;n) ∈ Type)
Proof
Definitions occuring in Statement :
uniform-continuity-pi: ucA(T;F;n),
nat: ℕ,
bool: 𝔹,
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,
uniform-continuity-pi: ucA(T;F;n),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
nat_wf,
bool_wf,
equal_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
subtype_rel_self
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
lambdaEquality,
because_Cache,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
applyEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
cumulativity,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[F:(\mBbbN{} {}\mrightarrow{} \mBbbB{}) {}\mrightarrow{} T]. \mforall{}[n:\mBbbN{}]. (ucA(T;F;n) \mmember{} Type)
Date html generated:
2017_04_17-AM-09_58_00
Last ObjectModification:
2017_02_27-PM-05_51_03
Theory : continuity
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