Nuprl Lemma : pseudo-bounded_wf
∀[S:Type]. pseudo-bounded(S) ∈ ℙ supposing S ⊆r ℕ
Proof
Definitions occuring in Statement :
pseudo-bounded: pseudo-bounded(S),
nat: ℕ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
pseudo-bounded: pseudo-bounded(S),
so_lambda: λ2x.t[x],
nat: ℕ,
subtype_rel: A ⊆r B,
int_upper: {i...},
so_apply: x[s]
Lemmas referenced :
all_wf,
nat_wf,
exists_wf,
int_upper_wf,
less_than_wf,
int_upper_subtype_nat,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
setElimination,
rename,
applyEquality,
functionExtensionality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[S:Type]. pseudo-bounded(S) \mmember{} \mBbbP{} supposing S \msubseteq{}r \mBbbN{}
Date html generated:
2016_12_12-AM-09_23_30
Last ObjectModification:
2016_11_22-PM-04_25_41
Theory : continuity
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