Nuprl Lemma : seq-item_wf
∀[T:Type]. ∀[s:sequence(T)]. ∀[i:ℕ||s||].  (s[i] ∈ T)
Proof
Definitions occuring in Statement : 
seq-item: s[i]
, 
seq-len: ||s||
, 
sequence: sequence(T)
, 
int_seg: {i..j-}
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
seq-item: s[i]
, 
sequence: sequence(T)
, 
pi2: snd(t)
, 
nat: ℕ
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
and: P ∧ Q
, 
seq-len: ||s||
, 
pi1: fst(t)
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
int_seg_wf, 
and_wf, 
le_wf, 
less_than_wf, 
seq-len_wf, 
nat_wf, 
sequence_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
sqequalHypSubstitution, 
productElimination, 
thin, 
applyEquality, 
functionExtensionality, 
hypothesisEquality, 
extract_by_obid, 
isectElimination, 
natural_numberEquality, 
setElimination, 
rename, 
hypothesis, 
dependent_set_memberEquality, 
independent_pairFormation, 
because_Cache, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
lambdaEquality, 
isect_memberEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}[s:sequence(T)].  \mforall{}[i:\mBbbN{}||s||].    (s[i]  \mmember{}  T)
Date html generated:
2018_07_25-PM-01_28_19
Last ObjectModification:
2018_06_11-PM-01_13_49
Theory : arithmetic
Home
Index