Nuprl Lemma : free-vars-aux_wf
∀[opr:Type]. ∀[t:term(opr)]. ∀[bnds:varname() List].
(free-vars-aux(bnds;t) ∈ {v:varname()| ¬(v = nullvar() ∈ varname())} List)
Proof
Definitions occuring in Statement :
free-vars-aux: free-vars-aux(bnds;t),
term: term(opr),
nullvar: nullvar(),
varname: varname(),
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
set: {x:A| B[x]} ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
coterm-fun: coterm-fun(opr;T),
varterm: varterm(v),
free-vars-aux: free-vars-aux(bnds;t),
mkterm: mkterm(opr;bts),
uiff: uiff(P;Q),
pi2: snd(t)
Lemmas referenced :
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
int_seg_properties,
int_seg_wf,
subtract-1-ge-0,
decidable__equal_int,
subtract_wf,
subtype_base_sq,
set_subtype_base,
int_subtype_base,
intformnot_wf,
intformeq_wf,
itermSubtract_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_subtract_lemma,
decidable__le,
decidable__lt,
istype-le,
subtype_rel_self,
term-ext,
subtype_rel_weakening,
term_wf,
coterm-fun_wf,
ext-eq_inversion,
term_size_var_lemma,
ifthenelse_wf,
deq-member_wf,
varname_wf,
var-deq_wf,
list_wf,
not_wf,
equal-wf-T-base,
nil_wf,
cons_wf,
nullvar_wf,
istype-void,
term_size_mkterm_lemma,
list-subtype,
l-union-list_wf,
equal_wf,
map_wf,
l_member_wf,
term-size-positive,
add-is-int-iff,
itermAdd_wf,
int_term_value_add_lemma,
false_wf,
summand-le-lsum,
term-size_wf,
pi2_wf,
rev-append_wf,
lsum_wf,
istype-nat,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
lambdaFormation_alt,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
isect_memberEquality_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isectIsTypeImplies,
inhabitedIsType,
functionIsTypeImplies,
productElimination,
unionElimination,
applyEquality,
instantiate,
because_Cache,
applyLambdaEquality,
dependent_set_memberEquality_alt,
productIsType,
promote_hyp,
hypothesis_subsumption,
setEquality,
baseClosed,
functionIsType,
equalityIstype,
productEquality,
closedConclusion,
pointwiseFunctionality,
baseApply,
setIsType,
independent_pairEquality,
addEquality,
universeEquality
Latex:
\mforall{}[opr:Type]. \mforall{}[t:term(opr)]. \mforall{}[bnds:varname() List].
(free-vars-aux(bnds;t) \mmember{} \{v:varname()| \mneg{}(v = nullvar())\} List)
Date html generated:
2020_05_19-PM-09_55_57
Last ObjectModification:
2020_03_12-AM-10_40_28
Theory : terms
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