Nuprl Lemma : hd_wf_listp
∀[A:Type]. ∀[l:A List+]. (hd(l) ∈ A)
Proof
Definitions occuring in Statement :
listp: A List+,
hd: hd(l),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
listp: A List+,
uimplies: b supposing a
Lemmas referenced :
hd_wf,
listp_properties,
listp_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
setElimination,
rename,
hypothesis,
independent_isectElimination,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[l:A List\msupplus{}]. (hd(l) \mmember{} A)
Date html generated:
2016_05_14-PM-01_30_31
Last ObjectModification:
2015_12_26-PM-05_23_09
Theory : list_1
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