Nuprl Lemma : member-free-vars-aux-not-bound
∀[opr:Type]. ∀t:term(opr). ∀bnds:varname() List. ∀v:varname(). ((v ∈ free-vars-aux(bnds;t)) ⇒ (¬(v ∈ bnds)))
Proof
Definitions occuring in Statement :
free-vars-aux: free-vars-aux(bnds;t),
term: term(opr),
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],
member: t ∈ T,
so_lambda: λ2x.t[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
not: ¬A,
false: False,
so_apply: x[s],
bound-term: bound-term(opr),
pi2: snd(t),
guard: {T},
free-vars-aux: free-vars-aux(bnds;t),
varterm: varterm(v),
or: P ∨ Q,
sq_type: SQType(T),
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
ifthenelse: if b then t else f fi ,
btrue: tt,
rev_implies: P ⇐ Q,
bfalse: ff,
squash: ↓T,
true: True,
respects-equality: respects-equality(S;T),
exists: ∃x:A. B[x],
mkterm: mkterm(opr;bts),
bool: 𝔹,
b-union: A ⋃ B,
varname: varname(),
nat: ℕ
Lemmas referenced :
term-induction,
list_wf,
varname_wf,
l_member_wf,
free-vars-aux_wf,
subtype_rel_list,
not_wf,
equal-wf-T-base,
nullvar_wf,
istype-void,
term_wf,
mkterm_wf,
bound-term_wf,
istype-universe,
deq-member_wf,
var-deq_wf,
null_nil_lemma,
btrue_wf,
member-implies-null-eq-bfalse,
nil_wf,
btrue_neq_bfalse,
assert_wf,
bnot_wf,
istype-assert,
bool_cases,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eqtt_to_assert,
assert-deq-member,
eqff_to_assert,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
member_singleton,
squash_wf,
true_wf,
subtype_rel_self,
iff_weakening_equal,
varterm_wf,
respects-equality-set-trivial2,
respects-equality-list,
member-map,
rev-append_wf,
map_wf,
member-l-union-list,
member-rev-append,
istype-atom,
product_subtype_base,
atom_subtype_base,
ifthenelse_wf,
tunion_subtype_base,
list_subtype_base,
nat_wf,
equal-wf-base,
pi2_wf,
equal_wf,
int_subtype_base,
istype-int,
le_wf,
set_subtype_base,
istype-nat,
length_wf_nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
lambdaEquality_alt,
functionEquality,
hypothesis,
applyEquality,
setEquality,
baseClosed,
independent_isectElimination,
setElimination,
rename,
setIsType,
universeIsType,
because_Cache,
functionIsType,
equalityIstype,
independent_functionElimination,
lambdaFormation_alt,
voidElimination,
productElimination,
instantiate,
universeEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
unionElimination,
cumulativity,
independent_pairFormation,
imageElimination,
natural_numberEquality,
imageMemberEquality,
inhabitedIsType,
productIsType,
promote_hyp,
dependent_pairFormation_alt,
independent_pairEquality,
spreadEquality,
inrFormation_alt,
productEquality,
atomEquality,
sqequalIntensionalEquality,
applyLambdaEquality,
hyp_replacement,
sqequalBase,
dependent_pairEquality_alt,
intEquality,
dependent_set_memberEquality_alt
Latex:
\mforall{}[opr:Type]
\mforall{}t:term(opr). \mforall{}bnds:varname() List. \mforall{}v:varname(). ((v \mmember{} free-vars-aux(bnds;t)) {}\mRightarrow{} (\mneg{}(v \mmember{} bnds)))
Date html generated:
2020_05_19-PM-09_56_00
Last ObjectModification:
2020_03_09-PM-04_09_10
Theory : terms
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