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
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