Nuprl Lemma : hd_member
∀[T:Type]. ∀L:T List. (hd(L) ∈ L) supposing ¬↑null(L)
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
hd: hd(l),
null: null(as),
list: T List,
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
or: P ∨ Q,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
cons: [a / b],
top: Top,
bfalse: ff,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
assert_wf,
null_wf,
list-cases,
null_nil_lemma,
product_subtype_list,
null_cons_lemma,
reduce_hd_cons_lemma,
cons_member,
l_member_wf,
not_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
lemma_by_obid,
isectElimination,
hypothesis,
rename,
unionElimination,
independent_functionElimination,
natural_numberEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
isect_memberEquality,
voidEquality,
because_Cache,
inlFormation,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. (hd(L) \mmember{} L) supposing \mneg{}\muparrow{}null(L)
Date html generated:
2016_05_14-AM-06_52_26
Last ObjectModification:
2015_12_26-PM-00_21_11
Theory : list_0
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