Nuprl Lemma : FormSafe2_wf
∀[C:Type]. ∀[f:Form(C)].  (FormSafe2(f) ∈ (Atom List) ⟶ 𝔹)
Proof
Definitions occuring in Statement : 
FormSafe2: FormSafe2(f)
, 
Form: Form(C)
, 
list: T List
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
atom: Atom
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
FormSafe2: FormSafe2(f)
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
top: Top
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
bor: p ∨bq
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
exists: ∃x:A. B[x]
, 
prop: ℙ
, 
or: P ∨ Q
, 
sq_type: SQType(T)
, 
guard: {T}
, 
bnot: ¬bb
, 
assert: ↑b
, 
false: False
, 
not: ¬A
, 
so_lambda: λ2x.t[x]
, 
band: p ∧b q
, 
so_apply: x[s]
, 
cons: [a / b]
, 
nat: ℕ
, 
le: A ≤ B
, 
decidable: Dec(P)
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
subtract: n - m
, 
less_than': less_than'(a;b)
, 
true: True
, 
listp: A List+
, 
has-value: (a)↓
, 
so_lambda: so_lambda(x,y,z.t[x; y; z])
, 
so_apply: x[s1;s2;s3]
, 
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w])
, 
so_apply: x[s1;s2;s3;s4]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
Lemmas referenced : 
Form_wf, 
top_wf, 
list_wf, 
bool_wf, 
subtype_rel_Form, 
bfalse_wf, 
null_wf3, 
eqtt_to_assert, 
assert_of_null, 
btrue_wf, 
eqff_to_assert, 
subtype_rel_list, 
equal_wf, 
bool_cases_sqequal, 
subtype_base_sq, 
bool_subtype_base, 
assert-bnot, 
equal-wf-base, 
list_subtype_base, 
atom_subtype_base, 
let_wf, 
list-diff_wf, 
atom-deq_wf, 
cons_wf, 
nil_wf, 
bor_wf, 
FormVar?_wf, 
eq_atom_wf, 
FormVar-name_wf, 
assert_of_eq_atom, 
bnot_wf, 
deq-member_wf, 
FormFvs_wf, 
hd_wf, 
listp_properties, 
list-cases, 
length_of_nil_lemma, 
product_subtype_list, 
length_of_cons_lemma, 
length_wf_nat, 
nat_wf, 
decidable__lt, 
false_wf, 
not-lt-2, 
condition-implies-le, 
minus-add, 
minus-one-mul, 
zero-add, 
minus-one-mul-top, 
add-commutes, 
add_functionality_wrt_le, 
add-associates, 
add-zero, 
le-add-cancel, 
less_than_wf, 
length_wf, 
value-type-has-value, 
list-value-type, 
band_wf, 
Form_ind_wf_simple
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
universeEquality, 
functionEquality, 
atomEquality, 
applyEquality, 
because_Cache, 
independent_isectElimination, 
lambdaEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
sqequalRule, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
equalityTransitivity, 
equalitySymmetry, 
productElimination, 
dependent_pairFormation, 
promote_hyp, 
dependent_functionElimination, 
instantiate, 
cumulativity, 
independent_functionElimination, 
baseClosed, 
hypothesis_subsumption, 
setElimination, 
rename, 
natural_numberEquality, 
addEquality, 
independent_pairFormation, 
intEquality, 
minusEquality, 
dependent_set_memberEquality, 
callbyvalueReduce, 
functionExtensionality
Latex:
\mforall{}[C:Type].  \mforall{}[f:Form(C)].    (FormSafe2(f)  \mmember{}  (Atom  List)  {}\mrightarrow{}  \mBbbB{})
Date html generated:
2018_05_21-PM-11_30_09
Last ObjectModification:
2017_10_13-PM-05_54_01
Theory : PZF
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