Nuprl Lemma : free-vars_wf
∀[opr:Type]. ∀[t:term(opr)].  (free-vars(t) ∈ {v:varname()| ¬(v = nullvar() ∈ varname())}  List)
Proof
Definitions occuring in Statement : 
free-vars: free-vars(t)
, 
term: term(opr)
, 
nullvar: nullvar()
, 
varname: varname()
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
not: ¬A
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
free-vars: free-vars(t)
Lemmas referenced : 
free-vars-aux_wf, 
nil_wf, 
varname_wf, 
term_wf, 
istype-universe
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeIsType, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
inhabitedIsType, 
instantiate, 
universeEquality
Latex:
\mforall{}[opr:Type].  \mforall{}[t:term(opr)].    (free-vars(t)  \mmember{}  \{v:varname()|  \mneg{}(v  =  nullvar())\}    List)
Date html generated:
2020_05_19-PM-09_56_09
Last ObjectModification:
2020_03_09-PM-04_09_14
Theory : terms
Home
Index