Nuprl Lemma : stump_wf
∀[T:Type]. ∀[t:wfd-tree(T)]. (stump(t) ∈ n:ℕ ⟶ (ℕn ⟶ T) ⟶ 𝔹)
Proof
Definitions occuring in Statement :
stump: stump(t),
wfd-tree: wfd-tree(T),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
stump: stump(t),
nat: ℕ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
bfalse: ff,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
false: False,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A,
ge: i ≥ j ,
int_upper: {i...},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
top: Top,
true: True,
sq_stable: SqStable(P),
squash: ↓T,
subtract: n - m,
so_apply: x[s]
Lemmas referenced :
wfd-tree-rec_wf,
nat_wf,
int_seg_wf,
bool_wf,
bfalse_wf,
eq_int_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
int_upper_subtype_nat,
false_wf,
le_wf,
nat_properties,
nequal-le-implies,
zero-add,
decidable__lt,
not-lt-2,
add_functionality_wrt_le,
add-commutes,
le-add-cancel,
lelt_wf,
subtract_wf,
decidable__le,
not-le-2,
sq_stable__le,
condition-implies-le,
minus-one-mul,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-member-int_seg2,
add-zero,
le-add-cancel2,
wfd-tree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
natural_numberEquality,
setElimination,
rename,
because_Cache,
cumulativity,
hypothesisEquality,
lambdaEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
dependent_pairFormation,
promote_hyp,
dependent_functionElimination,
instantiate,
independent_functionElimination,
voidElimination,
hypothesis_subsumption,
dependent_set_memberEquality,
independent_pairFormation,
applyEquality,
functionExtensionality,
isect_memberEquality,
voidEquality,
intEquality,
imageMemberEquality,
baseClosed,
imageElimination,
addEquality,
minusEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[t:wfd-tree(T)]. (stump(t) \mmember{} n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} \mBbbB{})
Date html generated:
2017_04_14-AM-07_45_14
Last ObjectModification:
2017_02_27-PM-03_16_17
Theory : co-recursion
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