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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