Nuprl Lemma : strong-continuity4_wf
∀[T:Type]. ∀[F:(ℕ ⟶ T) ⟶ ℕ]. (strong-continuity4(T;F) ∈ ℙ)
Proof
Definitions occuring in Statement :
strong-continuity4: strong-continuity4(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 :
all: ∀x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
uimplies: b supposing a,
so_apply: x[s],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
nat: ℕ,
strong-continuity4: strong-continuity4(T;F),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
isl_wf,
assert_wf,
subtype_rel_union,
false_wf,
int_seg_subtype_nat,
subtype_rel_dep_function,
equal_wf,
all_wf,
unit_wf2,
int_seg_wf,
nat_wf,
exists_wf
Rules used in proof :
universeEquality,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
inlEquality,
lambdaFormation,
independent_pairFormation,
independent_isectElimination,
functionExtensionality,
applyEquality,
productEquality,
lambdaEquality,
unionEquality,
hypothesisEquality,
cumulativity,
because_Cache,
rename,
setElimination,
natural_numberEquality,
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{}]. (strong-continuity4(T;F) \mmember{} \mBbbP{})
Date html generated:
2017_09_29-PM-06_05_22
Last ObjectModification:
2017_09_03-PM-09_54_30
Theory : continuity
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