Nuprl Lemma : hd_wf
∀[A:Type]. ∀[l:A List]. hd(l) ∈ A supposing ||l|| ≥ 1
Proof
Definitions occuring in Statement :
hd: hd(l)
,
length: ||as||
,
list: T List
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
,
ge: i ≥ j
,
member: t ∈ T
,
natural_number: $n
,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uimplies: b supposing a
,
all: ∀x:A. B[x]
,
or: P ∨ Q
,
ge: i ≥ j
,
le: A ≤ B
,
and: P ∧ Q
,
less_than': less_than'(a;b)
,
true: True
,
not: ¬A
,
implies: P
⇒ Q
,
false: False
,
cons: [a / b]
,
top: Top
,
prop: ℙ
Lemmas referenced :
list-cases,
length_of_nil_lemma,
product_subtype_list,
length_of_cons_lemma,
reduce_hd_cons_lemma,
ge_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
dependent_functionElimination,
unionElimination,
sqequalRule,
productElimination,
independent_functionElimination,
natural_numberEquality,
voidElimination,
promote_hyp,
hypothesis_subsumption,
isect_memberEquality,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[l:A List]. hd(l) \mmember{} A supposing ||l|| \mgeq{} 1
Date html generated:
2016_05_14-AM-06_34_28
Last ObjectModification:
2015_12_26-PM-00_35_46
Theory : list_0
Home
Index