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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