Nuprl Lemma : finite-type-iff-list
∀[T:Type]. (finite-type(T) ⇐⇒ ∃L:T List. ∀x:T. (x ∈ L))
Proof
Definitions occuring in Statement :
finite-type: finite-type(T),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
rev_implies: P ⇐ Q,
exists: ∃x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
finite-type: finite-type(T),
all: ∀x:A. B[x],
cardinality-le: |T| ≤ n
Lemmas referenced :
finite-type_wf,
exists_wf,
list_wf,
all_wf,
l_member_wf,
cardinality-le-list,
list-cardinality-le,
length_wf_nat,
cardinality-le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
sqequalRule,
lambdaEquality,
universeEquality,
dependent_functionElimination,
independent_functionElimination,
dependent_pairFormation
Latex:
\mforall{}[T:Type]. (finite-type(T) \mLeftarrow{}{}\mRightarrow{} \mexists{}L:T List. \mforall{}x:T. (x \mmember{} L))
Date html generated:
2016_05_14-PM-01_52_08
Last ObjectModification:
2015_12_26-PM-05_38_03
Theory : list_1
Home
Index