Nuprl Lemma : PZF-safe_wf
∀[C:Type]. ∀[phi:Form(C)]. ∀[vs:Atom List]. (PZF-safe(phi;vs) ∈ ℙ)
Proof
Definitions occuring in Statement :
PZF-safe: PZF-safe(phi;vs),
Form: Form(C),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
PZF-safe: PZF-safe(phi;vs)
Lemmas referenced :
FormSafe1_wf,
list_wf,
Form_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
applyEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
atomEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[C:Type]. \mforall{}[phi:Form(C)]. \mforall{}[vs:Atom List]. (PZF-safe(phi;vs) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-11_28_58
Last ObjectModification:
2017_10_12-PM-00_08_11
Theory : PZF
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