Nuprl Lemma : remove_leading_property2
∀[T:Type]. ∀[L:T List]. ∀[P:T ⟶ 𝔹]. ¬↑P[hd(remove_leading(x.P[x];L))] supposing ¬↑null(remove_leading(x.P[x];L))
Proof
Definitions occuring in Statement :
remove_leading: remove_leading(a.P[a];L),
null: null(as),
hd: hd(l),
list: T List,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
not: ¬A,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
top: Top,
prop: ℙ,
all: ∀x:A. B[x],
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
cons: [a / b],
bfalse: ff,
guard: {T},
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
decidable: Dec(P),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
less_than': less_than'(a;b),
listp: A List+
Lemmas referenced :
remove_leading_wf,
set_wf,
list_wf,
not_wf,
assert_wf,
null_wf3,
subtype_rel_list,
top_wf,
hd_wf,
listp_properties,
list-cases,
length_of_nil_lemma,
null_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
null_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,
equal_wf,
less_than_wf,
length_wf,
subtype_rel_set,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesis,
cumulativity,
functionEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
functionExtensionality,
dependent_functionElimination,
unionElimination,
independent_functionElimination,
natural_numberEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
setElimination,
rename,
addEquality,
independent_pairFormation,
intEquality,
minusEquality,
equalityTransitivity,
equalitySymmetry,
dependent_set_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[P:T {}\mrightarrow{} \mBbbB{}].
\mneg{}\muparrow{}P[hd(remove\_leading(x.P[x];L))] supposing \mneg{}\muparrow{}null(remove\_leading(x.P[x];L))
Date html generated:
2019_10_15-AM-11_08_45
Last ObjectModification:
2018_08_25-PM-00_07_18
Theory : general
Home
Index