Nuprl Lemma : alpha-rename-alist_wf
∀[opr:Type]. ∀[t:term(opr)]. ∀[L:varname() List].  (alpha-rename-alist(t;L) ∈ (varname() × varname()) List)
Proof
Definitions occuring in Statement : 
alpha-rename-alist: alpha-rename-alist(t;L)
, 
term: term(opr)
, 
varname: varname()
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
product: x:A × B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
alpha-rename-alist: alpha-rename-alist(t;L)
, 
so_lambda: λ2x y.t[x; y]
, 
has-value: (a)↓
, 
uimplies: b supposing a
, 
varname: varname()
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
so_apply: x[s1;s2]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
Lemmas referenced : 
list_accum_wf, 
varname_wf, 
list_wf, 
append_wf, 
all-vars_wf, 
nil_wf, 
value-type-has-value, 
bunion-value-type, 
nat_wf, 
atom-value-type, 
product-value-type, 
istype-atom, 
maybe_new_var_wf, 
cons_wf, 
pi2_wf, 
term_wf, 
istype-universe
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesis, 
closedConclusion, 
productEquality, 
hypothesisEquality, 
independent_pairEquality, 
because_Cache, 
sqequalRule, 
lambdaEquality_alt, 
productElimination, 
callbyvalueReduce, 
independent_isectElimination, 
atomEquality, 
universeIsType, 
productIsType, 
inhabitedIsType, 
lambdaFormation_alt, 
equalityIstype, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination, 
instantiate, 
universeEquality
Latex:
\mforall{}[opr:Type].  \mforall{}[t:term(opr)].  \mforall{}[L:varname()  List].
    (alpha-rename-alist(t;L)  \mmember{}  (varname()  \mtimes{}  varname())  List)
Date html generated:
2020_05_19-PM-09_57_09
Last ObjectModification:
2020_03_09-PM-04_09_34
Theory : terms
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