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
Home
Index