Nuprl Lemma : select_cons_hd
∀[T:Type]. ∀[a:T]. ∀[as:T List]. ∀[i:ℤ]. [a / as][i] = a ∈ T supposing i ≤ 0
Proof
Definitions occuring in Statement :
select: L[n],
cons: [a / b],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
top: Top,
prop: ℙ
Lemmas referenced :
select-cons-hd,
le_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
independent_isectElimination,
hypothesis,
natural_numberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
intEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[as:T List]. \mforall{}[i:\mBbbZ{}]. [a / as][i] = a supposing i \mleq{} 0
Date html generated:
2016_05_14-AM-06_36_27
Last ObjectModification:
2015_12_26-PM-00_33_59
Theory : list_0
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