Nuprl Lemma : Konig_wf
∀[k:ℕ]. (Konig(k) ∈ ℙ)
Proof
Definitions occuring in Statement : 
Konig: Konig(k)
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
Konig: Konig(k)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
nat: ℕ
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
Lemmas referenced : 
all_wf, 
nat_wf, 
int_seg_wf, 
bool_wf, 
le_wf, 
assert_wf, 
subtype_rel_dep_function, 
int_seg_subtype, 
false_wf, 
subtype_rel_self, 
not_wf, 
exists_wf, 
int_seg_subtype_nat
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
functionEquality, 
productEquality, 
hypothesis, 
natural_numberEquality, 
setElimination, 
rename, 
hypothesisEquality, 
because_Cache, 
lambdaEquality, 
applyEquality, 
dependent_pairEquality, 
independent_isectElimination, 
independent_pairFormation, 
lambdaFormation, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[k:\mBbbN{}].  (Konig(k)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-11_50_04
Last ObjectModification:
2015_12_28-PM-07_14_52
Theory : randomness
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