Nuprl Lemma : l_before_select
∀[T:Type]. ∀L:T List. ∀i,j:ℕ||L||. L[j] before L[i] ∈ L supposing j < i
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
select: L[n],
length: ||as||,
list: T List,
int_seg: {i..j-},
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
l_before: x before y ∈ l,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
int_seg: {i..j-}
Lemmas referenced :
member-less_than,
sublist_pair,
less_than_wf,
int_seg_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
hypothesis,
rename,
hypothesisEquality,
dependent_functionElimination,
setElimination,
natural_numberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}i,j:\mBbbN{}||L||. L[j] before L[i] \mmember{} L supposing j < i
Date html generated:
2016_05_14-AM-07_45_39
Last ObjectModification:
2015_12_26-PM-02_53_32
Theory : list_1
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