Nuprl Lemma : alpha-avoid-binders-disjoint
∀[opr:Type]. ∀L:varname() List. ((¬(nullvar() ∈ L)) ⇒ (∀t:term(opr). binders-disjoint(opr;L;alpha-avoid(L;t))))
Proof
Definitions occuring in Statement :
alpha-avoid: alpha-avoid(L;t),
binders-disjoint: binders-disjoint(opr;L;t),
term: term(opr),
nullvar: nullvar(),
varname: varname(),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
alpha-avoid: alpha-avoid(L;t),
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
uimplies: b supposing a,
istype: istype(T),
and: P ∧ Q,
cand: A c∧ B,
not: ¬A,
false: False,
alist-map: alist-map(eq;L),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q
Lemmas referenced :
alpha-rename-binders-disjoint,
alist-map_wf,
varname_wf,
var-deq_wf,
alpha-rename-alist_wf,
subtype_rel_dep_function,
l_member_wf,
all-vars_wf,
nullvar_wf,
term_wf,
istype-void,
list_wf,
istype-universe,
apply-alist_wf,
apply-alist-inl,
alpha-rename-alist-nonnullvar,
alpha-rename-alist-property,
member_append,
alpha-rename-alist-property2,
apply-alist-inr
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
applyEquality,
sqequalRule,
lambdaEquality_alt,
universeIsType,
setEquality,
setIsType,
independent_isectElimination,
setElimination,
rename,
because_Cache,
independent_functionElimination,
equalityIstype,
independent_pairFormation,
productElimination,
independent_pairEquality,
axiomEquality,
functionIsTypeImplies,
inhabitedIsType,
voidElimination,
functionIsType,
instantiate,
universeEquality,
unionElimination,
equalityTransitivity,
equalitySymmetry,
inlFormation_alt
Latex:
\mforall{}[opr:Type]
\mforall{}L:varname() List
((\mneg{}(nullvar() \mmember{} L)) {}\mRightarrow{} (\mforall{}t:term(opr). binders-disjoint(opr;L;alpha-avoid(L;t))))
Date html generated:
2020_05_19-PM-09_57_24
Last ObjectModification:
2020_03_09-PM-04_09_44
Theory : terms
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