Nuprl Lemma : PZF-safe-Fvs-subset

∀C:Type. ∀phi:Form(C). ∀vs:Atom List.  (PZF-safe(phi;vs) ⇒ l_subset(Atom;vs;FormFvs(phi)))


Proof




Definitions occuring in Statement :  PZF-safe: PZF-safe(phi;vs),  FormFvs: FormFvs(f),  Form: Form(C),  l_subset: l_subset(T;as;bs),  list: T List,  all: ∀x:A. B[x],  implies: P ⇒ Q,  atom: Atom,  universe: Type
Definitions unfolded in proof :  all: ∀x:A. B[x],  member: t ∈ T,  implies: P ⇒ Q,  FormSafe1: FormSafe1(f),  Form_ind: Form_ind,  PZF-safe: PZF-safe(phi;vs),  uall: ∀[x:A]. B[x],  prop: ℙ
Lemmas referenced :  FormSafe1-Fvs-subset,  PZF-safe_wf,  list_wf,  Form_wf
Rules used in proof :  cut,  introduction,  extract_by_obid,  sqequalSubstitution,  sqequalTransitivity,  computationStep,  sqequalReflexivity,  lambdaFormation,  hypothesis,  sqequalHypSubstitution,  dependent_functionElimination,  thin,  hypothesisEquality,  independent_functionElimination,  isectElimination,  cumulativity,  atomEquality,  universeEquality

Latex:
\mforall{}C:Type.  \mforall{}phi:Form(C).  \mforall{}vs:Atom  List.    (PZF-safe(phi;vs)  {}\mRightarrow{}  l\_subset(Atom;vs;FormFvs(phi)))



Date html generated: 2018_05_21-PM-11_29_03
Last ObjectModification: 2017_10_12-PM-00_08_45

Theory : PZF


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