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
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