### 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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