Nuprl Lemma : alpha-avoid_wf
∀[opr:Type]. ∀[t:term(opr)]. ∀[L:varname() List].  alpha-avoid(L;t) ∈ term(opr) supposing ¬(nullvar() ∈ L)
Proof
Definitions occuring in Statement : 
alpha-avoid: alpha-avoid(L;t)
, 
term: term(opr)
, 
nullvar: nullvar()
, 
varname: varname()
, 
l_member: (x ∈ l)
, 
list: T List
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
not: ¬A
, 
member: t ∈ T
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
alpha-avoid: alpha-avoid(L;t)
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
not: ¬A
, 
false: False
, 
alist-map: alist-map(eq;L)
Lemmas referenced : 
alpha-rename_wf, 
alist-map_wf, 
varname_wf, 
var-deq_wf, 
alpha-rename-alist_wf, 
nullvar_wf, 
l_member_wf, 
all-vars_wf, 
istype-void, 
list_wf, 
term_wf, 
istype-universe, 
apply-alist_wf, 
apply-alist-inl, 
alpha-rename-alist-nonnullvar
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
dependent_functionElimination, 
hypothesis, 
because_Cache, 
applyEquality, 
independent_isectElimination, 
lambdaFormation_alt, 
equalityIstype, 
universeIsType, 
setElimination, 
rename, 
setIsType, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionIsType, 
isect_memberEquality_alt, 
isectIsTypeImplies, 
inhabitedIsType, 
instantiate, 
universeEquality, 
independent_functionElimination, 
unionElimination, 
voidElimination
Latex:
\mforall{}[opr:Type].  \mforall{}[t:term(opr)].  \mforall{}[L:varname()  List].
    alpha-avoid(L;t)  \mmember{}  term(opr)  supposing  \mneg{}(nullvar()  \mmember{}  L)
Date html generated:
2020_05_19-PM-09_57_22
Last ObjectModification:
2020_03_09-PM-04_09_43
Theory : terms
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