Nuprl Lemma : whole_segment
∀T:Type. ∀as:T List. ((as[0..||as||-]) = as ∈ (T List))
Proof
Definitions occuring in Statement :
segment: as[m..n-],
length: ||as||,
list: T List,
all: ∀x:A. B[x],
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
top: Top
Lemmas referenced :
whole_segment-sq,
subtype_rel_list,
top_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
isectElimination,
hypothesis,
independent_isectElimination,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
universeEquality
Latex:
\mforall{}T:Type. \mforall{}as:T List. ((as[0..||as||\msupminus{}]) = as)
Date html generated:
2018_05_21-PM-00_19_29
Last ObjectModification:
2018_05_19-AM-06_59_46
Theory : list_0
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