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
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