Nuprl Lemma : alpha-rename-alist-property2
∀[opr:Type]
∀t:term(opr). ∀L:varname() List. ∀x:varname(). ((x ∈ L) ⇒ (∃x':varname(). (<x, x'> ∈ alpha-rename-alist(t;L))))
Proof
Definitions occuring in Statement :
alpha-rename-alist: alpha-rename-alist(t;L),
term: term(opr),
varname: varname(),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
pair: <a, b>,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
alpha-rename-alist: alpha-rename-alist(t;L),
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
exists: ∃x:A. B[x],
so_lambda: λ2x y.t[x; y],
has-value: (a)↓,
uimplies: b supposing a,
varname: varname(),
so_apply: x[s],
so_apply: x[s1;s2],
pi2: snd(t),
not: ¬A,
false: False,
iff: P ⇐⇒ Q,
and: P ∧ Q,
or: P ∨ Q,
rev_implies: P ⇐ Q,
squash: ↓T,
guard: {T},
true: True,
subtype_rel: A ⊆r B
Lemmas referenced :
list_induction,
varname_wf,
l_member_wf,
list_wf,
list_accum_wf,
value-type-has-value,
bunion-value-type,
nat_wf,
atom-value-type,
product-value-type,
istype-atom,
maybe_new_var_wf,
cons_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
cons_member,
list_accum_cons_lemma,
append_wf,
all-vars_wf,
term_wf,
istype-universe,
equal_wf,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal,
pi2_wf,
list_accum_nil_lemma
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
lambdaFormation_alt,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
sqequalRule,
lambdaEquality_alt,
functionEquality,
hypothesisEquality,
productEquality,
independent_pairEquality,
closedConclusion,
productElimination,
callbyvalueReduce,
independent_isectElimination,
atomEquality,
because_Cache,
inhabitedIsType,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
universeIsType,
voidElimination,
productIsType,
rename,
Error :memTop,
functionIsType,
instantiate,
universeEquality,
unionElimination,
dependent_pairFormation_alt,
inlFormation_alt,
applyEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
inrFormation_alt
Latex:
\mforall{}[opr:Type]
\mforall{}t:term(opr). \mforall{}L:varname() List. \mforall{}x:varname().
((x \mmember{} L) {}\mRightarrow{} (\mexists{}x':varname(). (<x, x'> \mmember{} alpha-rename-alist(t;L))))
Date html generated:
2020_05_19-PM-09_57_18
Last ObjectModification:
2020_03_09-PM-04_09_39
Theory : terms
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