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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