Nuprl Lemma : seq-nil_wf
∀[T:Type]. (seq-nil() ∈ sequence(T))
Proof
Definitions occuring in Statement :
seq-nil: seq-nil(),
sequence: sequence(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
int_seg: {i..j-},
prop: ℙ,
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
nat: ℕ,
sequence: sequence(T),
seq-nil: seq-nil(),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
int_seg_wf,
less_than_irreflexivity,
less_than_transitivity1,
le_wf,
false_wf
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
functionEquality,
voidElimination,
independent_functionElimination,
independent_isectElimination,
productElimination,
rename,
setElimination,
functionExtensionality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesis,
lambdaFormation,
independent_pairFormation,
natural_numberEquality,
dependent_set_memberEquality,
dependent_pairEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. (seq-nil() \mmember{} sequence(T))
Date html generated:
2018_07_25-PM-01_29_24
Last ObjectModification:
2018_06_18-PM-01_58_51
Theory : arithmetic
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