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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