Nuprl Lemma : strong-continuity2_wf
∀[T:Type]. ∀[F:(ℕ ⟶ T) ⟶ ℕ]. (strong-continuity2(T;F) ∈ ℙ)
Proof
Definitions occuring in Statement :
strong-continuity2: strong-continuity2(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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strong-continuity2: strong-continuity2(T;F),
nat: ℕ,
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
exists: ∃x:A. B[x]
Lemmas referenced :
exists_wf,
nat_wf,
int_seg_wf,
unit_wf2,
all_wf,
equal_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
isect_wf,
assert_wf,
isl_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
natural_numberEquality,
setElimination,
rename,
because_Cache,
cumulativity,
hypothesisEquality,
unionEquality,
lambdaEquality,
productEquality,
applyEquality,
functionExtensionality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
inlEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[F:(\mBbbN{} {}\mrightarrow{} T) {}\mrightarrow{} \mBbbN{}]. (strong-continuity2(T;F) \mmember{} \mBbbP{})
Date html generated:
2016_12_12-AM-09_22_26
Last ObjectModification:
2016_11_22-AM-11_37_45
Theory : continuity
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