Nuprl Lemma : varterm_wf
∀[opr:Type]. ∀[v:varname()].  varterm(v) ∈ term(opr) supposing ¬(v = nullvar() ∈ varname())
Proof
Definitions occuring in Statement : 
varterm: varterm(v)
, 
term: term(opr)
, 
nullvar: nullvar()
, 
varname: varname()
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
not: ¬A
, 
member: t ∈ T
, 
universe: Type
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
varterm: varterm(v)
, 
coterm-fun: coterm-fun(opr;T)
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
, 
subtype_rel: A ⊆r B
, 
guard: {T}
Lemmas referenced : 
term-ext, 
nullvar_wf, 
istype-void, 
list_wf, 
varname_wf, 
term_wf, 
ext-eq_inversion, 
coterm-fun_wf, 
subtype_rel_weakening, 
istype-universe
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
inlEquality_alt, 
dependent_set_memberEquality_alt, 
sqequalRule, 
functionIsType, 
equalityIstype, 
inhabitedIsType, 
productIsType, 
universeIsType, 
productEquality, 
applyEquality, 
independent_isectElimination, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
because_Cache, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
instantiate, 
universeEquality
Latex:
\mforall{}[opr:Type].  \mforall{}[v:varname()].    varterm(v)  \mmember{}  term(opr)  supposing  \mneg{}(v  =  nullvar())
Date html generated:
2020_05_19-PM-09_53_39
Last ObjectModification:
2020_03_09-PM-04_08_16
Theory : terms
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