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
, 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
Lemmas referenced : 
list_wf, 
segment_factor, 
non_neg_length, 
length_wf_nat, 
length_wf, 
iff_weakening_equal, 
lapp_fact_b
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
equalityEquality, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
dependent_functionElimination, 
because_Cache, 
introduction, 
natural_numberEquality, 
because_SupInf, 
equalityTransitivity, 
equalitySymmetry, 
independent_isectElimination, 
productElimination, 
independent_functionElimination, 
universeEquality
Latex:
\mforall{}T:Type.  \mforall{}as:T  List.    ((as[0..||as||\msupminus{}])  =  as)
Date html generated:
2016_05_16-AM-07_42_36
Last ObjectModification:
2015_12_28-PM-05_41_38
Theory : list_2
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