Nuprl Lemma : hd?_wf
∀[T:Type]. ∀[L:T List]. (hd?(L) ∈ T?)
Proof
Definitions occuring in Statement :
hd?: hd?(L),
list: T List,
uall: ∀[x:A]. B[x],
unit: Unit,
member: t ∈ T,
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
hd?: hd?(L),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
all: ∀x:A. B[x],
implies: P ⇒ Q,
exposed-bfalse: exposed-bfalse,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
false: False,
cons: [a / b],
guard: {T},
nat: ℕ,
le: A ≤ B,
decidable: Dec(P),
subtract: n - m,
less_than': less_than'(a;b),
true: True,
listp: A List+
Lemmas referenced :
null_wf3,
subtype_rel_list,
top_wf,
bool_wf,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
list_wf,
eqtt_to_assert,
assert_of_null,
it_wf,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
hd_wf,
listp_properties,
list-cases,
length_of_nil_lemma,
nil_wf,
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,
equal_wf,
less_than_wf,
length_wf,
unit_wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
applyEquality,
hypothesis,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
baseClosed,
cumulativity,
independent_functionElimination,
productElimination,
inrEquality,
independent_pairFormation,
impliesFunctionality,
inlEquality,
dependent_functionElimination,
promote_hyp,
hypothesis_subsumption,
setElimination,
rename,
natural_numberEquality,
addEquality,
intEquality,
minusEquality,
dependent_set_memberEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. (hd?(L) \mmember{} T?)
Date html generated:
2018_05_21-PM-07_33_23
Last ObjectModification:
2017_07_26-PM-05_08_17
Theory : general
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